An rectangular area of 25 square meters, around an ancient historical site, is to be fenced to protect the artifacts. The sides with length x cost $ 34/ m and the other two sides cost $ 26 /m.

a. Write an expression for the cost as a function of x.

C(x) =

b. The value of x for minimum cost is x =

1 answer

x w = 25 so w = 25/x

2 * 34* x + 2 * 26 * w = cost = c

c = 68 x + 52 w

c = 68 x + 52 (25/x)
c = 68 x + 1300/x

==========================
dc/dx = 0 for min = 68 - 1300/x^2

x^2 = 1300/68
x = 4.37