A rectangular milk carton has a square base of side length centimetres and height…

MATHEMATICS · Subjective · AoPS · Mathematics · More Variables · x Marks the Spot

Problem

A rectangular milk carton has a square base of side length

x

centimetres and height

h

centimetres. The carton must hold exactly 1 000 cm

^{3}

of liquid. The material for the base and the four sides costs $0.02 per cm

^{2}

, while the material for the lid costs $0.05 per cm

^{2}

. Write a simplified expression for the total cost

C(x)

(in dollars) as a function of

x

only.