Do Hom ?https:/ MA TH110 K009 Win 18 Edwina Watson &1 5/11/18 11:07 PM lusTM Hom

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Do Hom ?https:/ MA TH110 K009 Win 18 Edwina Watson &1 5/11/18 11:07 PM lusTM Homework: Week 14: Homework 9.5 14 Score: 0 of 1 pt ection 99.6.35 HW Score: 80.83%, 16 17 of 20 pts Palo Alto College is planning to construct a rectangular parking lot on land bordered on one side by a other three sides. What dimensions should the lot have if the enclosed area is to be ection 9 highway The plan is to use 440 feet of fencing to fence off the a maximum? est 7 The width is feet. The length is feet.(Let the longer side be the length and the shorter side the width) Enter your answer in the edit fields and then click Check Answer All parts showing

Explanation / Answer

Let the length and the width of the rectangular plot be x and y ft. respectively. Then x+2y = 440 so thay y = 440-x. The area of the rectangular plot is A = length* width = xy = x(440-x) = 440x-x2. Then dA/dx = 440-2x and d2A/dx2 = -2. The area of the rectangular plot will be maximum when dA/dx = 0, i.e. when x = 220 and when d2A/dx2is negative. Since, d2A/dx2 is negative regardless of the value of x, hence A will be maximum when the length is 220 ft. and the width is (440-220)/2 = 110 ft.

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