Asmall shelter for delicate plants is to be constructed of thin plastic material. it will have a square end and a rectangular top and back, with an open bottom and front as shown in the figure. the total are of the four plastic sides is to be 1200in^2. a) express the volume of the shelter as a function of the depth x. b) what dimensions will maximize the volume of the shelter?

Part A

The four plastic sides comprises of two equal squares of area each and two equal rectangles of area each.

Given that the total area of the four plastic sides is to be , thus:



The volume of the figure is given by: Volume = Area of base x depth



Part B:

For maximum volume, the derivative of V with respect to x will equal 0.



But dimensions has to be positive, thus the value of x which produces maximum volume is x = 14.14

Recall that



Therefore, the dimensions that will maximize the volume of the shelter is x = 14.14 and y = 28.29