Introduction to Linear Programming Dominik Scheder Products - PowerPoint PPT Presentation

Introduction to Linear Programming Dominik Scheder

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1 × +4 ×

1 × +4 × =

1 × +4 × = = 14 ×

1 × +4 × = = 14 × 8 × +4 × = = 28 ×

1 × +4 × = = 14 × 8 × +4 × = = 28 × 1 × +2 × = = 7 ×

1 × +4 × = = 14 × 8 × +4 × = = 28 × 1 × +2 × = = 7 ×

1 × +4 × = = 14 × 8 × +4 × = = 28 × 1 × +2 × = = 7 ×

1 × +4 × = = 14 × 8 × +4 × = = 28 × 1 × +2 × = = 7 ×

1 × +4 × = = 14 × 8 × +4 × = = 28 × 1 × +2 × = = 7 ×

1 × +4 × = = 14 × 8 × +4 × = = 28 × 1 × +2 × = = 7 ×

1 × +4 × = = 14 × 8 × +4 × = = 28 × 1 × +2 × = = 7 × 98 ×

7 1 × +4 × = = 14 × is a feasible solution . 0 8 × +4 × = = 28 × 0 1 × +2 × = = 7 × 98 ×

1 × +4 × = = 14 × 8 × +4 × = = 28 × 1 × +2 × = = 7 ×

1 × +4 × = = 14 × 8 × +4 × = = 28 × 1 × +2 × = = 7 ×

1 × +4 × = = 14 × 8 × +4 × = = 28 × 1 × +2 × = = 7 ×

1 × +4 × = = 14 × 8 × +4 × = = 28 × 1 × +2 × = = 7 ×

1 × +4 × = = 14 × 8 × +4 × = = 28 × 1 × +2 × = = 7 ×

1 × +4 × = = 14 × 8 × +4 × = = 28 × 1 × +2 × = = 7 ×

1 × +4 × = = 14 × 8 × +4 × = = 28 × 1 × +2 × = = 7 ×

1 × +4 × = = 14 × 8 × +4 × = = 28 × 1 × +2 × = = 7 ×

4 1 × +4 × = = 14 × is an infeasible solution . 4 8 × +4 × = = 28 × 0 1 × +2 × = = 7 ×

By growing 7 units of rice and nothing else, the farmer makes 98 units of money.

By growing 7 units of rice and nothing else, the farmer makes 98 units of money. Can you compute the optimum?

Upper Bounds An Economists Perspective

1 × +4 × = = 14 × 8 × +4 × = = 28 × 1 × +2 × = = 7 ×

1 × +4 × = = 14 × 8 × +4 × = = 28 × ??? 1 × +2 × = = 7 ×

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for for ???

for for ???

for for ???

35 × 2 + 28 × 5 = 210 for for ???

35 × 2 + 28 × 5 = 210 for for ??? A Good Deal?

for for

1 × +4 × = = 14 × for for

1 × +4 × = = 14 × 1 × +4 × = 20 × for for

1 × +4 × = = 14 × 1 × +4 × = 20 × for for

1 × +4 × = = 14 × 1 × +4 × = 20 × 8 × +4 × = = 28 × for for

1 × +4 × = = 14 × 1 × +4 × = 20 × 8 × +4 × = = 28 × 8 × +4 × = 36 × for for

1 × +4 × = = 14 × 1 × +4 × = 20 × 8 × +4 × = = 28 × 8 × +4 × = 36 × for for

1 × +4 × = = 14 × 1 × +4 × = 20 × 8 × +4 × = = 28 × 8 × +4 × = 36 × for for 1 × +2 × = = 7 ×

1 × +4 × = = 14 × 1 × +4 × = 20 × 8 × +4 × = = 28 × 8 × +4 × = 36 × for for 1 × +2 × = = 7 × 1 × +2 × = 12 ×

1 × +4 × = = 14 × 1 × +4 × = 20 × 8 × +4 × = = 28 × 8 × +4 × = 36 × for for 1 × +2 × = = 7 × 1 × +2 × = 12 ×

35 × 2 + 28 × 5 = 210 for A Good Deal? for ??? The best you can get!

1 × +4 × = = 14 × 8 × +4 × = = 28 × 1 × +2 × = = 7 × 98 ×

1 × +4 × = = 14 × 8 × +4 × = = 28 × 1 × +2 × = = 7 × 98 ×

1 × +4 × = = 14 × for 8 × +4 × = = 28 × for 1 × +2 × = = 7 × 98 × 35 × 2 + 28 × 5 = 210

1 × +4 × = = 14 × for 8 × +4 × = = 28 × for 1 × +2 × = = 7 × 98 × 35 × 2 + 28 × 5 = 210 98 × ≤ 210 ≤