# maxima/minima problems

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A regular box is open at the top and has a square base. To construct the box costs \$4 a square foot for the base and \$3 a square foot for its sides. Find the cost of the least expensive box and the dimensions of this least expensive box.

There is not enough data given to set up the problem.
Wasn't the volume of the box given?

volume is 144cubic feet

volume is 144 cubic feet

ahh, now we got something to work with, hope it is not too late

let each side of the base be x, let the height be y
given: (x^2)y = 144 ----> y=144/x^2

Cost = 4(x^2) + 3(4xy)
=4x^2 + 12x(144/x^2)
= 4x^2 + 1728/x

Differentiate the Cost equation, set that result equal to zero and solve for x
(I got x=6)

thanx. i got 432 for the price and 4 for y

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