A fence is to be built to enclose a rectangular area of 800 square feet. The fence along 3 sides is to be made of material $4 per foot. The material for the fourth side costs $12 per foot. Find the dimensions of the rectangle that will allow for the most economical fence to be built.

Answer 1

if the expensive side is x and the other dimension is y, then the cost c is

c = 4(x+2y) + 12x

But, we know the area is xy=800, so y = 800/x and the cost is now

c = 4(x+1600/x) + 12x
minimum cost when dc/dx=0, so we need

dc/dx = -16(400-x^2)/x^2
dc/dx=0 when x=20, so the fence is 20x40

Answer 2

Don't have an answer. Just need to know how the calculations are done.

Answer 3

. Afence is to be built to enclose a rectangular area of 800 square feet. The fence along three sides is to be made of material that costs Birr2 per foot. The material for the fourth side costs Birr6 per foot. Find the dimension of the rectangular that will allow the most economical fence to be built.