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Anonymous asked in Science & MathematicsEngineering · 2 months ago

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 = $____

1 Answer

  • 2 months ago
    Favorite 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.

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