A rectangular storage container with an open top is to have a volume of 28 cubic meters. The length of its base is twice the width?

Question

A rectangular storage container with an open top is to have a volume of 28 cubic meters. The length of its base is twice the width. Material for the base costs 11 dollars per square meter. Material for the sides costs 7 dollars per square meter. Find the cost of materials for the cheapest such container.

Answer 1

Let the width of the base be "x". Then length = 2x. The height = 28/(2x^2) = 14/(x^2).

Cost of materials, say, C.

C = (2x^2)*11+(6x)(14/x^2)*7. Now find x for least C.

C = 22x^2 +588/x,

22x^2-Cx+588 = 0. For real values of x: ∆=b^2-4ac≥0,

C^2 ≥ 4*22*588.

C ≥ 227.4741

Least cost = $ 227.47