Bill wants to fence in his rectangular garden so his precious produce will be protected. Three sides of the fence will be constructed with wire at $2 per linear foot and the fourth side will be constructed of wood fencing at a cost of 6$ per linear foot.If he has $400 to spend on the fencing what dimensions would maximize the area he can plant?

Question

Bill wants to fence in his rectangular garden so his precious produce will be protected. Three sides of the fence will be constructed with wire at $2 per linear foot and the fourth side will be constructed of wood fencing at a cost of 6$ per linear foot.If he has $400 to spend on the fencing what dimensions would maximize the area he can plant?

i have my cost function as C(x)= $2(2l+w)+6w
wouldn't i set the cost to 400 after simplifying? how do i get the area..i'm very confused. Help please.

Answer 1

yes. you know that

2(2l+w)+6w = 600
4l+8w = 600
l+2w = 150
so, l = 150-2w

The area is

a = lw = (150-2w)w = 150w - 2w^2

So, find w which makes a the maximum. That will be at the vertex of the parabola.