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 $ 10 per foot, and fencing for the other two sides is $ 3 per foot. The four corner posts are $ 20 each. Let x be the length of one of the sides perpendicular to the river.

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

b) What is the domain of C?

a) C (x) = 15000/x + 6x + 80

b) Domain of C (x) { R x>0 }

Step-by-step explanation:

We have:

Enclosed area = 1500 ft² = x*y from which y = 1500 / x (a) where x is perpendicular to the river

Cost = cost of sides of fenced area perpendicular to the river + cost of side parallel to river + cost of 4 post then

Cost = 10*y + 2*3*x + 4*20 and accoding to (a) y = 1500/x

Then

C (x) = 10 * (1500/x) + 6*x + 80

C (x) = 15000/x + 6x + 80

Domain of C (x) { R x>0 }