Mathematics

Problem

A shipping crate has a square base with side length

x

feet and no top. The crate must have a volume of

500\text{ ft}^3

. The wood for the base costs \

10 per square foot, and the wood for the four sides costs

4 per square foot. Which of the following expressions gives the total material cost

C

, in dollars, as a function of

x

after the volume condition has been used to eliminate the height? a)

C(x)=10x^{2}+\dfrac{8000}{x}

C(x)=10x^{2}+\dfrac{2000}{x}

C(x)=14x^{2}+\dfrac{8000}{x}

C(x)=10x^{2}+\dfrac{8000}{x^{2}}