A rectangular �eld is to be fenced o� along the bank of a river; no fence is required along the bank

Question

of the river. The material for the fence costs 8 dollars per running foot for the two ends and 16
dollars per running foot for the side parallel to the river. If the area of the �eld is to be 12,000
sq. feet and the cost of the fence is not to exceed 3,520 dollars, what are the restrictions on the
dimensions of the �eld?

I'm not sure how to solve this. help me pleasee. thank you

Answer 1

What's an eld ?

let the side parallel to the rive by y ft
let the other sides be x ft each
so xy = 1200
y = 1200/x

cost of fence = 16y + 8(2x)
= 16(1200/x) + 16x
= 19200/x + 16x

d(cos)/dx = -19200/x^2 + 16
= 0 for a min cost.
16x^2 = 19200
Can you finish it?