If the bottom has side x and the box has height h, then
x^2 h = 6, so h = 6/x^2
the cost function is
c = 8x^2 + 3*4*xh = 8x^2 + 72/x = 8(x^2 + 9/x)
so find where dc/dx = 0
You are constructing a box for your cat to sleep in. The box has no top (just a bottom and four sides).
The plush material for the square bottom of the box costs $8.00 per square foot and the material for the sides costs $3.00 per square foot. You need a box with a volume of 6 cubic feet.
Find the dimensions of the box that minimize the cost function. Then, find the minimum cost.
A. 0.72 x 0.72 x 2.88 with a cost of about $29.03
B. 2 x 2 x 1.5 with a cost of $68.00.
C. 1.75 x 1.75 x 1.96 with a cost of about $65.66.
D. 1.651 x 1.651 x 2.201 with a cost of about $65.42.
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