SOLUTION: A rectangular storage container with an open top is to have a volume of 10 m3. The length of this base is twice the width. Material for the base costs $20 per square meter. Materia

Question 907313: A rectangular storage container with an open top is to have a volume of 10 m3. The length of this base is twice the width. Material for the base costs $20 per square meter. Material for the sides costs $12 per square meter. Find the cost of materials for the cheapest such container. (Round your answer to the nearest cent.)

Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
x for length, y for width,
x=2y
volume is 10 cubic meters, so if for z height,
xyz=10

Finding z:

Still more information is needed to have a better relationship among the three dimensions.

These are the costs of the different rectangular parts altogether:

and if you substitute for y,

-----This cost written in terms of y and z.

You can use the earlier found, to either substitute for y or for z in the cost function.
First, simplify the "10" equation to .
; substitute for z, done here.

cost,
.

This is probably meant as a calculus problem using the derivative .
Form the derivative, and solve for y in to find and check extremes (for a minimum value for c).

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