Posted by **Sunny** on Thursday, April 4, 2013 at 12:49am.

Ignoring the walls’ thickness, determine the outside dimensions that will minimize a closed box’s cost if it has a square base and top, if its volume is 32 cubic meters, and if the cost per square meter for the top, bottom, and sides respectively are $.03, $.04, and $.05.

(solve step by step please!)

- Math -
**wodolo**, Thursday, April 4, 2013 at 1:05am
4/2

- Math -
**Sunny**, Thursday, April 4, 2013 at 1:06am
can you explain how you got that please?

- Math -
**Reiny**, Thursday, April 4, 2013 at 8:40am
let the base be x m by x m, let the height be y m

x^2 y = 32

y = 32/x^2

cost = cost of base + cost of top + cost of 4 sides

= .03x^2 + .04x^2 +4(.05)xy

= .07x^2 + .2x(32/x^2)

= .07x^2 + 6.4/x

d(cost)/dx = .14x - 6.4/x^2

= 0 for a min of cost

6.4/x^2 = .14x

x^3 = .896

x = .896^(1/3) = appr .964 m

then y = 32/.964^2 = appr 34.43 m

The answer seems unreasonable, but I just can't find any errors in my solution.

Even wrote it out on paper.

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