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September 23, 2014

September 23, 2014

Posted by **math dave** on Wednesday, April 17, 2013 at 10:36pm.

- math -
**Reiny**, Wednesday, April 17, 2013 at 11:18pmlet the base be x by x

let the height be y

x^ y = volume

x^2 y = 320

y = 320/x^2

cost = 15x^2 + 10x^2 + 4(2.5)xy

= 25x^2 + 10x(320/x^2)

= 25x^2 + 3200/x

d(cost)/dx = 50x - 3200/x^2 = 0 for a min of cost

50x = 3200/x^2

x^3 = 64

x = 4

then y = 320/16 = 20

the box should have a base of 4 by 4 and a height of 20 units

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