Question

a farmer wishes to fence off a rectangular plot of land, using an existing wall as one of the sides . the total are enclosed must be 600 square yards. the fence on the side parallel to the wall will cost 20$ per yard, while the fences on the other side will cost 30$ per yard.

What should the dimension of the rectangle be in order to minimize the total cost of the fence?

Answer 1

let the two equal width be x
let the single side by y

xy = 600
y = 600/x

cost = 20y + 30x
= 20(600/x) + 30x
d(cost)/dx = -12000/x^2 + 30
= 0 for a min of cost
30 = 12000/x^2
x^2 = 400
x = 20

the two equal sides are 20 yds each, and the long side is 600/20 = 30 yds.