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 $ 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?

Answer 1

Answer:

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 }