Posted by **Megan** on Tuesday, May 27, 2008 at 7:34pm.

The material for the base of a box will cost three times as much as the material for the sides and top of the box. The box must have a volume of 200 meters cubed. Find the most efficient way to built this box.

- Math-Optimization -
**Reiny**, Tuesday, May 27, 2008 at 10:53pm
Having seen and done hundreds of this type of question, I am pretty sure that the base is a square.

Else you don't have enough information to solve the question.

let the side of the base be x

let its height be y

so (x^2)y = 200 ---> y = 200/x^2

Cost = 3 money units(base) + 1 money unit(4 sides) + 1 money unit(top)

Cost = 3x^2 + 4(xy) + x^2

C = 4x^2 + 4xy

= 4x^2 + 4x(200/x^2)

= 4x^2 + 800/x

C' = 8x - 800/x^2 = 0 for a min of C

8x = 800/x^2

x^3 = 100

x = 4.64 and y = 9.28

PS, if the volume had been 2000 m^3 we would have had nice integer values.

Are you sure you did not make a typo?

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