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

Optimization 2 October 31, 2016 1

Optimization 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? 2

Optimization 2 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. 3

Optimization 2 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? 4

Optimization 2 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? 5

Optimization 2 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. 6

Optimization 2 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? 7