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Math Question please help?
A rectangular storage container with an open top is to have a volume of 10 𝑚^3. The length of its base is twice the width. Material for the base costs $12 per 𝑚^2. Material for the sides costs $1.6 per 𝑚^2. Find the dimensions of the container which will minimize cost and the minimum cost.
base length = ____ m
base width = ____ m
height = ____ m
minimum cost = $____
- az_lenderLv 72 months agoFavorite Answer
Height = 10/(W*2W) = 5/W^2.
C = $12*2W^2 + $1.6*(2H*W + 2H*2W)
= $24W^2 + $9.6W(5/W^2)
= $24W^2 + $48/W.
dC/dW = $48W - $48/W^2.
This will be 0 when W = 1, L = 2, H = 5.
Minimum cost = $72.