a rectangular lot adjacent to a highway is to be enclosed by a fencing cost $ 2.50 per foot.along the highway $1.50 per foot on the other sides find the dimension of the largest lot that can be fenced off for $270.

Question

a rectangular lot adjacent to a highway is to be enclosed by a fencing cost $ 2.50  per foot.along the highway $1.50 per foot on the other sides find the dimension of the largest lot that can be fenced off for $270.

Thank you God bless. Badly need it

Steve · Accepted Answer

If the dimension along the road is x, then we have a cost of

2.50x + 1.50x + 2*1.50y
= 4x + 3y = 270

The area is

a = xy = x(270-4x)/3
= 90x - 4/3 x^2

da/dx = 90 - 8/3 x

now you can find x and y for maximum area