A shipping crate has a square base with side length feet and no top

MATHEMATICS · Single correct · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

A shipping crate has a square base with side length xx feet and no top. The crate must have a volume of 500 ft3500\text{ ft}^3. The wood for the base costs 10 dollars per square foot, and the wood for the four sides costs 4 dollars per square foot. Which of the following expressions gives the total material cost CC, in dollars, as a function of xx after the volume condition has been used to eliminate the height? (a) C(x)=10x2+8000xC(x)=10x^2+\dfrac{8000}{x} (b) C(x)=10x2+2000xC(x)=10x^2+\dfrac{2000}{x} (c) C(x)=14x2+8000xC(x)=14x^2+\dfrac{8000}{x} (d) C(x)=10x2+8000x2C(x)=10x^2+\dfrac{8000}{x^2}

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