Express the cost C in terms of x

Question

An open top box with a square base of length x and height y is to be constructed so that its volume is V=1860cm³. If the cost of the material for the base of the box is $0.46 per square centimeter and the cost of the sides is $1.03 per square centimeter, express the cost C of the box in terms of the length of the base x.

C(x)=??

Answer 1

C(x) = Cost of the bottom + 4(cost of the sides)

C(x) = 0.46(Area of the bottom)+4(1.03)(Area of the sides)

C(x) = 0.46(x²)+4(1.03)(xy)

This has a y in it, to make it only in terms of x, we can use the other information on Volume

V=lwh Plugging in what we know

1860=(x)(x)(y)

1860=x²y Solve for y

y=1860/x²

Substitute this into the equation:

C(x) = 0.46(x²)+4(1.03)(x)(1860/x²) Simplify by multiplication and canceling out x/x

C(x) = 0.46x²+7663.2/x