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March 30, 2015

March 30, 2015

Posted by **diwas** on Tuesday, November 13, 2012 at 10:06pm.

- math -
**Reiny**, Tuesday, November 13, 2012 at 10:44pmlength --- x

width --- y

height ---- 1.5y

1.5xy^2 = 2.4

x = 2.4/(1.5y^2) = 8/(5y^2)

Assuming the cost is a function of the surface area (SA)

SA = 2xy + 2(1.5xy) + 2(1.5y^2)

= 2xy + 3xy + 3y^2

= 5y((8/(5y^2) + 3y^2

= 8/y + 3y^2

d(SA)/dy = -8/y^2 + 6y = 0 for a min of SA

8/y^2 = 6y

6y^3 = 8

y^3 = 8/6

y = 2/6^(1/3) = 1.1006.. = appr 1.1

1.5y = 1.65

x = 8/(5(1.1006..)^2) = 1.32

so

length = 1.32

width = 1.1

height = 1.65

check: V = 1.32x1.1x1.65 = appr 2.3958 , close to 2.4, not bad

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