Optimization 2 October 31, 2016 1 Optimization 2 October 31, 2016 - - PDF document

Optimization 2 1 October 31, 2016

Optimization 2 2 October 31, 2016

A rectangular pool with an area of 50 sq m is surrounded by a wooden walkway 1 m wide on one pair of opposite sides, and 2 m wide on the other two sides. What are the dimensions of the pool that minimize the area of the walkway?

Optimization 2 3 October 31, 2016

A 5 ft tall fence is located 4 ft from the house. Find the length of the shortest ladder that extends from the ground, over the fence to the house.

Optimization 2 4 October 31, 2016

A metal gutter is made by folding a 9 inch piece of metal. The gutters have a 3 inch base, and two 3 inch sides folded up at an angle. What angle maximizes the cross­sectional area of the gutter?

Optimization 2 5 October 31, 2016

Anne stands on one bank of a 2000 ft wide river, and needs to reach a point 4000 ft up the bank on the opposite side of the river. If Anne walks at 300 ft/min and paddles her stand up surfboard at 200 ft/min, where should she land to minimize the duration of the trip?

Optimization 2 6 October 31, 2016

A cone is constructed from a circular piece of metal with radius 5 inches, and cutting away a sector, folding up and welding the seam. Find the radius and height of the cone with maximal volume that can be found this way.

Optimization 2 7 October 31, 2016

A steel pipe is carried down a hallway 9 ft wide. At the end of the hall, there is a perpendicular 6 ft wide hallway. What is the length of the longest pipe that can be carried horizontally around the corner?