Write a function​ C(x) that describes the cost of the project.

Question

A rectangular area adjacent to a river is fenced​ in; no fence is needed on the river side. The enclosed area is 1500 square feet. Fencing for the side parallel to the river is $8 per​ foot, and fencing for the other two sides is $3 per foot. The four corner posts are $30 each. Let x be the length of one of the sides perpendicular to the river.

Answer 1

xy = 1500

y = 1500/x

2x(3) + 8y = Cost = C

C= 6x + 8(1500/x) = 6x+12000/x

take the derivative and set = 0

C' = 6 -12000/x^2 = 0

6x^2 = 12000

x^2 = 2,000

x = sqr2000 = 20sqr5 = about 45 feet for perpendicular sides

y =1500/45 = about 33 1/3 feet for the side parallel to the river

minimum Cost =about 6(45) + 8(33.3) + 4(30) = $647