Optimization Help: Total Cost

Calculus
Tutor: None Selected Time limit: 1 Day

Apr 18th, 2015

Area base = LxW = 2WxW = 2W^2

Area of the 2 long sides = 2xLxH = 2x2WxH = 4WH

Area of the 2 short sides = 2xWxH = 2WH

Total area of sides = 6WH

but volume is 24, so

2W^2*H = 24

H = 12/W^2

Cost = (2W^2)(10) + (6WH)(6)

substitute H = 12/W^2

C(w) = 20W^2 + 36W(12/W^2)

C(w) = 20W^2 + 432/W

C'(w) = 40W- 432/W^2 = 0

40W^3 - 432 = 0

W^3 = 432/40 = 10.8

W = 2.21 meters

C(2.21) = 20(2.21^2) + 432/2.21 = $293.16


Apr 17th, 2015

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Apr 18th, 2015
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