mu construction 9.5 14

Question

MU is planning to construct a rectangular parking lot on land bordered on one side by a highway. The plan is to use 760
feet of fencing to fence off the other three sides. What dimensions should the lot have if the enclosed area is to be a? maximum?
The width is ____feet.The length is _______
feet.

Answer 1

Let x = length of the side parallel to the highway

     y = length of each of the other two sides

 

Then x + 2y = 760, so 2y = 760 - x.

 

                                  y = 380 - 0.5x

 

Maximize A = xy = x(380 - 0.5x)

 

The graph of the area function is a parabola opening downward.  The maximum occurs halfway between the x-intercepts (0 and 760).   

 

So, the area is maximized when x = 380 ft and y = 190 ft.