[PPT] - MATH 105: Finite Mathematics 3-3: Linear Programming Story Problems PowerPoint Presentation

SLIDE 1

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

MATH 105: Finite Mathematics 3-3: Linear Programming Story Problems

Prof. Jonathan Duncan

Walla Walla College

Winter Quarter, 2006

SLIDE 2

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Outline

1

Investment Allocation

2

Widget Production

3

Hotel Occupancy

4

Cruise Ships

5

Conclusion

SLIDE 3

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Outline

1

Investment Allocation

2

Widget Production

3

Hotel Occupancy

4

Cruise Ships

5

Conclusion

SLIDE 4

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Investments: Problem Set-up

Example

An investment broker wants to invest up to $20,000. She can purchase type A bonds yielding a 10% return and she can purchase a more risky type B bounds yielding a 15% return. She wants to invest at least as much in the type A bond as in the type B bond to reduce her risk. The minimum investment for the type A bond is $5,000, and there are only $8,000 worth of type B bonds available. How much should the broker invest in each type of bond to maximize her returns?

SLIDE 5

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Investments: Problem Set-up

Example

An investment broker wants to invest up to $20,000. She can purchase type A bonds yielding a 10% return and she can purchase a more risky type B bounds yielding a 15% return. She wants to invest at least as much in the type A bond as in the type B bond to reduce her risk. The minimum investment for the type A bond is $5,000, and there are only $8,000 worth of type B bonds available. How much should the broker invest in each type of bond to maximize her returns? Let: x be amount invested in A y the amount invested in B Objective: Maximize 0.10x + 0.15y Constraints:            x + y ≤ 20, 000 x ≥ y x ≥ 5, 000 y ≤ 8, 000 y ≥

SLIDE 6

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Investments: Locating Corner Points

Example Continued. . . The region obtained from the constraints is shown below.

SLIDE 7

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Investments: Locating Corner Points

Example Continued. . . The region obtained from the constraints is shown below.

✁

✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁

y=x y=8000 x=5000 x+y=20000

SLIDE 8

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Investments: Locating Corner Points

Example Continued. . . The region obtained from the constraints is shown below.

✁

✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁

y=x y=8000 x=5000 x+y=20000

Intersecting Lines Point x = 5000 and y = 0 (5000, 0) x = 5000 and y = x (5000, 5000) y = 8000 and y = x (8000, 8000) y = 8000 and x + y = 20000 (12000, 8000) y = 0 and x + y = 20000 (20000, 0)

SLIDE 9

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Investments: Locating Corner Points

Example Continued. . . The region obtained from the constraints is shown below.

✁

✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁

y=x y=8000 x=5000 x+y=20000

Intersecting Lines Point x = 5000 and y = 0 (5000, 0) x = 5000 and y = x (5000, 5000) y = 8000 and y = x (8000, 8000) y = 8000 and x + y = 20000 (12000, 8000) y = 0 and x + y = 20000 (20000, 0)

SLIDE 10

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Investments: Locating Corner Points

Example Continued. . . The region obtained from the constraints is shown below.

✁

✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁

y=x y=8000 x=5000 x+y=20000

Intersecting Lines Point x = 5000 and y = 0 (5000, 0) x = 5000 and y = x (5000, 5000) y = 8000 and y = x (8000, 8000) y = 8000 and x + y = 20000 (12000, 8000) y = 0 and x + y = 20000 (20000, 0)

SLIDE 11

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Investments: Locating Corner Points

Example Continued. . . The region obtained from the constraints is shown below.

✁

✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁

y=x y=8000 x=5000 x+y=20000

Intersecting Lines Point x = 5000 and y = 0 (5000, 0) x = 5000 and y = x (5000, 5000) y = 8000 and y = x (8000, 8000) y = 8000 and x + y = 20000 (12000, 8000) y = 0 and x + y = 20000 (20000, 0)

SLIDE 12

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Investments: Locating Corner Points

Example Continued. . . The region obtained from the constraints is shown below.

✁

✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁

y=x y=8000 x=5000 x+y=20000

Intersecting Lines Point x = 5000 and y = 0 (5000, 0) x = 5000 and y = x (5000, 5000) y = 8000 and y = x (8000, 8000) y = 8000 and x + y = 20000 (12000, 8000) y = 0 and x + y = 20000 (20000, 0)

SLIDE 13

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Investments: Locating Corner Points

Example Continued. . . The region obtained from the constraints is shown below.

✁

✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁

y=x y=8000 x=5000 x+y=20000

Intersecting Lines Point x = 5000 and y = 0 (5000, 0) x = 5000 and y = x (5000, 5000) y = 8000 and y = x (8000, 8000) y = 8000 and x + y = 20000 (12000, 8000) y = 0 and x + y = 20000 (20000, 0)

SLIDE 14

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Investments: The Solution

Example Continued. . . Finally, plug each corner point into the objective function.

Corner Point Value of 0.10x + 0.15y (5000, 0) .1(5000) + .15(0) = $500 (5000, 5000) .10(5000) + .15(5000) = $1350 (8000, 8000) .10(8000) + .15(8000) = $2000 (12000, 8000) .10(12000) + .15(8000) = $2400 (20000, 0) .10(20000) + .15(0) = $2000

Maximum profit of $2,400 when she invests $12,000 in type A and $8,000 in type B bonds.

SLIDE 15

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Investments: The Solution

Example Continued. . . Finally, plug each corner point into the objective function.

Corner Point Value of 0.10x + 0.15y (5000, 0) .1(5000) + .15(0) = $500 (5000, 5000) .10(5000) + .15(5000) = $1350 (8000, 8000) .10(8000) + .15(8000) = $2000 (12000, 8000) .10(12000) + .15(8000) = $2400 (20000, 0) .10(20000) + .15(0) = $2000

Maximum profit of $2,400 when she invests $12,000 in type A and $8,000 in type B bonds.

SLIDE 16

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Investments: The Solution

Example Continued. . . Finally, plug each corner point into the objective function.

Corner Point Value of 0.10x + 0.15y (5000, 0) .1(5000) + .15(0) = $500 (5000, 5000) .10(5000) + .15(5000) = $1350 (8000, 8000) .10(8000) + .15(8000) = $2000 (12000, 8000) .10(12000) + .15(8000) = $2400 (20000, 0) .10(20000) + .15(0) = $2000

Maximum profit of $2,400 when she invests $12,000 in type A and $8,000 in type B bonds.

SLIDE 17

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Investments: The Solution

Example Continued. . . Finally, plug each corner point into the objective function.

Corner Point Value of 0.10x + 0.15y (5000, 0) .1(5000) + .15(0) = $500 (5000, 5000) .10(5000) + .15(5000) = $1350 (8000, 8000) .10(8000) + .15(8000) = $2000 (12000, 8000) .10(12000) + .15(8000) = $2400 (20000, 0) .10(20000) + .15(0) = $2000

Maximum profit of $2,400 when she invests $12,000 in type A and $8,000 in type B bonds.

SLIDE 18

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Investments: The Solution

Example Continued. . . Finally, plug each corner point into the objective function.

Corner Point Value of 0.10x + 0.15y (5000, 0) .1(5000) + .15(0) = $500 (5000, 5000) .10(5000) + .15(5000) = $1350 (8000, 8000) .10(8000) + .15(8000) = $2000 (12000, 8000) .10(12000) + .15(8000) = $2400 (20000, 0) .10(20000) + .15(0) = $2000

Maximum profit of $2,400 when she invests $12,000 in type A and $8,000 in type B bonds.

SLIDE 19

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Investments: The Solution

Example Continued. . . Finally, plug each corner point into the objective function.

Corner Point Value of 0.10x + 0.15y (5000, 0) .1(5000) + .15(0) = $500 (5000, 5000) .10(5000) + .15(5000) = $1350 (8000, 8000) .10(8000) + .15(8000) = $2000 (12000, 8000) .10(12000) + .15(8000) = $2400 (20000, 0) .10(20000) + .15(0) = $2000

Maximum profit of $2,400 when she invests $12,000 in type A and $8,000 in type B bonds.

SLIDE 20

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Investments: The Solution

Example Continued. . . Finally, plug each corner point into the objective function.

Corner Point Value of 0.10x + 0.15y (5000, 0) .1(5000) + .15(0) = $500 (5000, 5000) .10(5000) + .15(5000) = $1350 (8000, 8000) .10(8000) + .15(8000) = $2000 (12000, 8000) .10(12000) + .15(8000) = $2400 (20000, 0) .10(20000) + .15(0) = $2000

Maximum profit of $2,400 when she invests $12,000 in type A and $8,000 in type B bonds.

SLIDE 21

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Outline

1

Investment Allocation

2

Widget Production

3

Hotel Occupancy

4

Cruise Ships

5

Conclusion

SLIDE 22

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Widgets: Problem Set-up

Example

Ms. Li produces widgets. To make 100 left-handed widgets she uses 1

pound of metal and 5 pounds of fiberglass. To make 100 right-handed widgets she uses 2 pounds of metal and 3 pounds of fiberglass. Each week Ms. Li has 65 poinds of metal and 150 pounds of fiberglass

delivered. She makes a profit of $2.50 per right-handed widget and $2.00

per left-handed widget. How many widgets of each type should Ms. Li produce to maximize profit?

SLIDE 23

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Widgets: Problem Set-up

Example

Ms. Li produces widgets. To make 100 left-handed widgets she uses 1

pound of metal and 5 pounds of fiberglass. To make 100 right-handed widgets she uses 2 pounds of metal and 3 pounds of fiberglass. Each week Ms. Li has 65 poinds of metal and 150 pounds of fiberglass

delivered. She makes a profit of $2.50 per right-handed widget and $2.00

per left-handed widget. How many widgets of each type should Ms. Li produce to maximize profit? Let: x be # 100s of right-handed y be # 100s of left-handed Objective: Maximize 250x + 200y Constraints:        x + 2y ≤ 65 5x + 3y ≤ 150 x ≥ y ≥

SLIDE 24

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Widgets: Locating Corner Points

Example Continued. . . The region obtained from the constraints is shown below.

SLIDE 25

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Widgets: Locating Corner Points

Example Continued. . . The region obtained from the constraints is shown below.

✁

✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁

5x+3y=150 x+2y=65

SLIDE 26

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Widgets: Locating Corner Points

Example Continued. . . The region obtained from the constraints is shown below.

✁

✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁

5x+3y=150 x+2y=65

Intersecting Lines Point y = 0 and 5x + 3y = 150 (30, 0) x = 0 and y = 0 (0, 0) x = 0 and x + 2y = 65 (0, 32.5) 5x + 3y = 150 and x + 2y = 65 (15, 25)

SLIDE 27

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Widgets: Locating Corner Points

Example Continued. . . The region obtained from the constraints is shown below.

✁

✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁

5x+3y=150 x+2y=65

Intersecting Lines Point y = 0 and 5x + 3y = 150 (30, 0) x = 0 and y = 0 (0, 0) x = 0 and x + 2y = 65 (0, 32.5) 5x + 3y = 150 and x + 2y = 65 (15, 25)

SLIDE 28

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Widgets: Locating Corner Points

Example Continued. . . The region obtained from the constraints is shown below.

✁

✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁

5x+3y=150 x+2y=65

Intersecting Lines Point y = 0 and 5x + 3y = 150 (30, 0) x = 0 and y = 0 (0, 0) x = 0 and x + 2y = 65 (0, 32.5) 5x + 3y = 150 and x + 2y = 65 (15, 25)

SLIDE 29

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Widgets: Locating Corner Points

Example Continued. . . The region obtained from the constraints is shown below.

✁

✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁

5x+3y=150 x+2y=65

Intersecting Lines Point y = 0 and 5x + 3y = 150 (30, 0) x = 0 and y = 0 (0, 0) x = 0 and x + 2y = 65 (0, 32.5) 5x + 3y = 150 and x + 2y = 65 (15, 25)

SLIDE 30

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Widgets: Locating Corner Points

Example Continued. . . The region obtained from the constraints is shown below.

✁

✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁

5x+3y=150 x+2y=65

Intersecting Lines Point y = 0 and 5x + 3y = 150 (30, 0) x = 0 and y = 0 (0, 0) x = 0 and x + 2y = 65 (0, 32.5) 5x + 3y = 150 and x + 2y = 65 (15, 25)

SLIDE 31

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Widgets: The Solution

Example Continued. . . Finally, plug each corner point into the objective function.

Corner Point Value of 250x + 200y (30, 0) 250(30) + 200(0) = $7500 (0, 0) 250(0) + 200(0) = $0 (0, 32.5) 250(0) + 200(32.5) = $6500 (15, 25) 250(15) + 200(25) = $8750

Maximum profit of $8750 when Ms. Li makes 150 right- and 250 left-handed widgets.

SLIDE 32

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Widgets: The Solution

Example Continued. . . Finally, plug each corner point into the objective function.

Corner Point Value of 250x + 200y (30, 0) 250(30) + 200(0) = $7500 (0, 0) 250(0) + 200(0) = $0 (0, 32.5) 250(0) + 200(32.5) = $6500 (15, 25) 250(15) + 200(25) = $8750

Maximum profit of $8750 when Ms. Li makes 150 right- and 250 left-handed widgets.

SLIDE 33

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Widgets: The Solution

Example Continued. . . Finally, plug each corner point into the objective function.

Corner Point Value of 250x + 200y (30, 0) 250(30) + 200(0) = $7500 (0, 0) 250(0) + 200(0) = $0 (0, 32.5) 250(0) + 200(32.5) = $6500 (15, 25) 250(15) + 200(25) = $8750

Maximum profit of $8750 when Ms. Li makes 150 right- and 250 left-handed widgets.

SLIDE 34

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Widgets: The Solution

Example Continued. . . Finally, plug each corner point into the objective function.

Corner Point Value of 250x + 200y (30, 0) 250(30) + 200(0) = $7500 (0, 0) 250(0) + 200(0) = $0 (0, 32.5) 250(0) + 200(32.5) = $6500 (15, 25) 250(15) + 200(25) = $8750

Maximum profit of $8750 when Ms. Li makes 150 right- and 250 left-handed widgets.

SLIDE 35

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Widgets: The Solution

Example Continued. . . Finally, plug each corner point into the objective function.

Corner Point Value of 250x + 200y (30, 0) 250(30) + 200(0) = $7500 (0, 0) 250(0) + 200(0) = $0 (0, 32.5) 250(0) + 200(32.5) = $6500 (15, 25) 250(15) + 200(25) = $8750

Maximum profit of $8750 when Ms. Li makes 150 right- and 250 left-handed widgets.

SLIDE 36

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Widgets: The Solution

Example Continued. . . Finally, plug each corner point into the objective function.

Corner Point Value of 250x + 200y (30, 0) 250(30) + 200(0) = $7500 (0, 0) 250(0) + 200(0) = $0 (0, 32.5) 250(0) + 200(32.5) = $6500 (15, 25) 250(15) + 200(25) = $8750

Maximum profit of $8750 when Ms. Li makes 150 right- and 250 left-handed widgets.

SLIDE 37

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Outline

1

Investment Allocation

2

Widget Production

3

Hotel Occupancy

4

Cruise Ships

5

Conclusion

SLIDE 38

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Hotels: Problem Set-up

Example

A company owns two hotels: the Luxar and the Grand. The Luxar has 10 single rooms and 12 double rooms on each of its 10 floors. The Grand has 12 single rooms and 8 double rooms on each of its 15 floors. The floors can be staffed individually. It costs $10,000 per floor to staff the Luxar and $8,50 per floor to staff the Grand. If there is a demand for 100 single rooms and 80 double rooms, how many floors should be staffed in each hotel to meet the demand while minimizing costs?

SLIDE 39

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Hotels: Problem Set-up

Example

A company owns two hotels: the Luxar and the Grand. The Luxar has 10 single rooms and 12 double rooms on each of its 10 floors. The Grand has 12 single rooms and 8 double rooms on each of its 15 floors. The floors can be staffed individually. It costs $10,000 per floor to staff the Luxar and $8,50 per floor to staff the Grand. If there is a demand for 100 single rooms and 80 double rooms, how many floors should be staffed in each hotel to meet the demand while minimizing costs? Let: x be # floors in Luxar y be # floors in Grand Objective: Minimize 10000x + 8500y Constraints:                10x + 12y ≥ 100 12x + 8y ≥ 80 x ≤ 10 y ≤ 15 x ≥ y ≥

SLIDE 40

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Hotels: Locating Corner Points

Example Continued. . . The region obtained from the constraints is shown below.

SLIDE 41

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Hotels: Locating Corner Points

Example Continued. . . The region obtained from the constraints is shown below.

✁

✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁

y=15 x=10 12x+8y=80 10x+12y=100

SLIDE 42

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Hotels: Locating Corner Points

Example Continued. . . The region obtained from the constraints is shown below.

✁

✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁

y=15 x=10 12x+8y=80 10x+12y=100

Intersecting Lines Point x = 0 and y = 15 (0, 15) x = 10 and y = 15 (10, 15) x = 10 and y = 0 (10, 0) 12x + 8y = 80 and 10x + 12y = 100 “

10 4 , 25 4

” 12x + 8y = 80 and x = 0 (0, 10)

SLIDE 43

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Hotels: Locating Corner Points

Example Continued. . . The region obtained from the constraints is shown below.

✁

✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁

y=15 x=10 12x+8y=80 10x+12y=100

Intersecting Lines Point x = 0 and y = 15 (0, 15) x = 10 and y = 15 (10, 15) x = 10 and y = 0 (10, 0) 12x + 8y = 80 and 10x + 12y = 100 “

10 4 , 25 4

” 12x + 8y = 80 and x = 0 (0, 10)

SLIDE 44

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Hotels: Locating Corner Points

Example Continued. . . The region obtained from the constraints is shown below.

✁

✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁

y=15 x=10 12x+8y=80 10x+12y=100

Intersecting Lines Point x = 0 and y = 15 (0, 15) x = 10 and y = 15 (10, 15) x = 10 and y = 0 (10, 0) 12x + 8y = 80 and 10x + 12y = 100 “

10 4 , 25 4

” 12x + 8y = 80 and x = 0 (0, 10)

SLIDE 45

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Hotels: Locating Corner Points

Example Continued. . . The region obtained from the constraints is shown below.

✁

✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁

y=15 x=10 12x+8y=80 10x+12y=100

Intersecting Lines Point x = 0 and y = 15 (0, 15) x = 10 and y = 15 (10, 15) x = 10 and y = 0 (10, 0) 12x + 8y = 80 and 10x + 12y = 100 “

10 4 , 25 4

” 12x + 8y = 80 and x = 0 (0, 10)

SLIDE 46

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Hotels: Locating Corner Points

Example Continued. . . The region obtained from the constraints is shown below.

✁

✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁

y=15 x=10 12x+8y=80 10x+12y=100

Intersecting Lines Point x = 0 and y = 15 (0, 15) x = 10 and y = 15 (10, 15) x = 10 and y = 0 (10, 0) 12x + 8y = 80 and 10x + 12y = 100 “

10 4 , 25 4

” 12x + 8y = 80 and x = 0 (0, 10)

SLIDE 47

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Hotels: Locating Corner Points

Example Continued. . . The region obtained from the constraints is shown below.

✁

✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁

y=15 x=10 12x+8y=80 10x+12y=100

Intersecting Lines Point x = 0 and y = 15 (0, 15) x = 10 and y = 15 (10, 15) x = 10 and y = 0 (10, 0) 12x + 8y = 80 and 10x + 12y = 100 “

10 4 , 25 4

” 12x + 8y = 80 and x = 0 (0, 10)

SLIDE 48

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Hotels: The Solution

Example Continued. . . Finally, plug each corner point into the objective function.

Corner Point Value of 10000x + 8500y (0, 15) 10000(0) + 8500(15) = $127,500 (10, 15) 10000(10) + 8500(15) = $227,500 (10, 0) 10000(10) + 8500(0) = $100,000 “

10 4 , 25 4

” 10000 “

10 4

” + 8500 “

25 4

” = $78,125 (0, 10) 10000(0) + 8500(10) = $85,000 (3, 6) 10000(3) + 8500(6) = $81,000 (2, 7) 10000(2) + 85000(7) = $79,000

Minimum cost of $79,000 when 2 floors in the Luxar and 7 in the Grand are opened.

SLIDE 49

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Hotels: The Solution

Example Continued. . . Finally, plug each corner point into the objective function.

Corner Point Value of 10000x + 8500y (0, 15) 10000(0) + 8500(15) = $127,500 (10, 15) 10000(10) + 8500(15) = $227,500 (10, 0) 10000(10) + 8500(0) = $100,000 “

10 4 , 25 4

” 10000 “

10 4

” + 8500 “

25 4

” = $78,125 (0, 10) 10000(0) + 8500(10) = $85,000 (3, 6) 10000(3) + 8500(6) = $81,000 (2, 7) 10000(2) + 85000(7) = $79,000

Minimum cost of $79,000 when 2 floors in the Luxar and 7 in the Grand are opened.

SLIDE 50

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Hotels: The Solution

Example Continued. . . Finally, plug each corner point into the objective function.

Corner Point Value of 10000x + 8500y (0, 15) 10000(0) + 8500(15) = $127,500 (10, 15) 10000(10) + 8500(15) = $227,500 (10, 0) 10000(10) + 8500(0) = $100,000 “

10 4 , 25 4

” 10000 “

10 4

” + 8500 “

25 4

” = $78,125 (0, 10) 10000(0) + 8500(10) = $85,000 (3, 6) 10000(3) + 8500(6) = $81,000 (2, 7) 10000(2) + 85000(7) = $79,000

Minimum cost of $79,000 when 2 floors in the Luxar and 7 in the Grand are opened.

SLIDE 51

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Hotels: The Solution

Example Continued. . . Finally, plug each corner point into the objective function.

Corner Point Value of 10000x + 8500y (0, 15) 10000(0) + 8500(15) = $127,500 (10, 15) 10000(10) + 8500(15) = $227,500 (10, 0) 10000(10) + 8500(0) = $100,000 “

10 4 , 25 4

” 10000 “

10 4

” + 8500 “

25 4

” = $78,125 (0, 10) 10000(0) + 8500(10) = $85,000 (3, 6) 10000(3) + 8500(6) = $81,000 (2, 7) 10000(2) + 85000(7) = $79,000

Minimum cost of $79,000 when 2 floors in the Luxar and 7 in the Grand are opened.

SLIDE 52

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Hotels: The Solution

Example Continued. . . Finally, plug each corner point into the objective function.

Corner Point Value of 10000x + 8500y (0, 15) 10000(0) + 8500(15) = $127,500 (10, 15) 10000(10) + 8500(15) = $227,500 (10, 0) 10000(10) + 8500(0) = $100,000 “

10 4 , 25 4

” 10000 “

10 4

” + 8500 “

25 4

” = $78,125 (0, 10) 10000(0) + 8500(10) = $85,000 (3, 6) 10000(3) + 8500(6) = $81,000 (2, 7) 10000(2) + 85000(7) = $79,000

Minimum cost of $79,000 when 2 floors in the Luxar and 7 in the Grand are opened.

SLIDE 53

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Hotels: The Solution

Example Continued. . . Finally, plug each corner point into the objective function.

Corner Point Value of 10000x + 8500y (0, 15) 10000(0) + 8500(15) = $127,500 (10, 15) 10000(10) + 8500(15) = $227,500 (10, 0) 10000(10) + 8500(0) = $100,000 “

10 4 , 25 4

” 10000 “

10 4

” + 8500 “

25 4

” = $78,125 (0, 10) 10000(0) + 8500(10) = $85,000 (3, 6) 10000(3) + 8500(6) = $81,000 (2, 7) 10000(2) + 85000(7) = $79,000

Minimum cost of $79,000 when 2 floors in the Luxar and 7 in the Grand are opened.

SLIDE 54

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Hotels: The Solution

Example Continued. . . Finally, plug each corner point into the objective function.

Corner Point Value of 10000x + 8500y (0, 15) 10000(0) + 8500(15) = $127,500 (10, 15) 10000(10) + 8500(15) = $227,500 (10, 0) 10000(10) + 8500(0) = $100,000 “

10 4 , 25 4

” 10000 “

10 4

” + 8500 “

25 4

” = $78,125 (0, 10) 10000(0) + 8500(10) = $85,000 (3, 6) 10000(3) + 8500(6) = $81,000 (2, 7) 10000(2) + 85000(7) = $79,000

Minimum cost of $79,000 when 2 floors in the Luxar and 7 in the Grand are opened.

SLIDE 55

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Hotels: The Solution

Example Continued. . . Finally, plug each corner point into the objective function.

Corner Point Value of 10000x + 8500y (0, 15) 10000(0) + 8500(15) = $127,500 (10, 15) 10000(10) + 8500(15) = $227,500 (10, 0) 10000(10) + 8500(0) = $100,000 “

10 4 , 25 4

” 10000 “

10 4

” + 8500 “

25 4

” = $78,125 (0, 10) 10000(0) + 8500(10) = $85,000 (3, 6) 10000(3) + 8500(6) = $81,000 (2, 7) 10000(2) + 85000(7) = $79,000

Minimum cost of $79,000 when 2 floors in the Luxar and 7 in the Grand are opened.

SLIDE 56

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Hotels: The Solution

Example Continued. . . Finally, plug each corner point into the objective function.

Corner Point Value of 10000x + 8500y (0, 15) 10000(0) + 8500(15) = $127,500 (10, 15) 10000(10) + 8500(15) = $227,500 (10, 0) 10000(10) + 8500(0) = $100,000 “

10 4 , 25 4

” 10000 “

10 4

” + 8500 “

25 4

” = $78,125 (0, 10) 10000(0) + 8500(10) = $85,000 (3, 6) 10000(3) + 8500(6) = $81,000 (2, 7) 10000(2) + 85000(7) = $79,000

Minimum cost of $79,000 when 2 floors in the Luxar and 7 in the Grand are opened.

SLIDE 57

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Outline

1

Investment Allocation

2

Widget Production

3

Hotel Occupancy

4

Cruise Ships

5

Conclusion

SLIDE 58

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Cruise Ships: Problem Set-up

Example

Columbus Cruise Lines offers one-week cruises on three ships: the Nina, Pinta, and Santa Maria. The Nina has 500 regular rooms and 200 deluxe

rooms. The Pinta has 400 regular and 400 deluxe rooms. The Santa

Maria has 800 regular and 500 deluxe rooms. The costs to run the ships are $100,000 a week, $120,000 a week, and $180,000 a week respectively. For how many weeks of the 12 week season should each ship be active to meet the season’s demand for 12,000 regular rooms and 8,000 deluxe rooms while minimizing costs?

SLIDE 59

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Outline

1

Investment Allocation

2

Widget Production

3

Hotel Occupancy

4

Cruise Ships

5

Conclusion

SLIDE 60

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Important Concepts

Things to Remember from Section 3-3

1 Be sure to define variables. 2 Find the objective function and specify minimize or maximize. 3 Identify the constraints using a table, when possible.

SLIDE 61

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Important Concepts

Things to Remember from Section 3-3

1 Be sure to define variables. 2 Find the objective function and specify minimize or maximize. 3 Identify the constraints using a table, when possible.

SLIDE 62

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Important Concepts

Things to Remember from Section 3-3

1 Be sure to define variables. 2 Find the objective function and specify minimize or maximize. 3 Identify the constraints using a table, when possible.

SLIDE 63

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Important Concepts

Things to Remember from Section 3-3

1 Be sure to define variables. 2 Find the objective function and specify minimize or maximize. 3 Identify the constraints using a table, when possible.

SLIDE 64

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion

Next Time. . .

This is the last section of the course. Please see the review sheet as you start to study for the final. For next time Review for the Final

SLIDE 65

Investment Allocation Widget Production Hotel Occupancy Cruise Ships Conclusion