Problema Solution
A 298-ft^3 pool is to be built with a square bottom of side length x. The sides are built with tiles and the bottom with cement. The cost per unit of tiles is $7/ft^2 while the cost of the bottom is $2/ft^2. Write the total cost C as a function of x.
Answer provided by our tutors
let
x = the side length of the square bottom, x>0
h = the height of the pool, h>0
V = 298 ft^3 the volume of the pool
V = x^2*h
x^2*h = 298
h = 298/x^2
C(x) = 2*x^2 + 7*4(x*h)
C(x) = 2x^2 + 28x(298/x^2)
C(x) = 2x^2 + 8344/x
the total cost as a function of x is: C(x) = 2x^2 + 8344/x.