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CALC

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An open box is to be constructed so that the length of the base is 4 times larger than the width of the base. If the cost to construct the base is 5 dollars per square foot and the cost to construct the four sides is 3 dollars per square foot, determine the dimensions for a box to have volume = 25 cubic feet which would minimize the cost of construction.

Values for dimension of the base are: ?

The height of the box is: ?

  • CALC -

    l=5w

    costbase= lw*5
    cost sides=3(2lh+2wh)

    volume=lwh
    25=lwh
    or h= 25/wl

    costtotal=5(lw*5)+3(2l*25/wl + 2w*25/wl)
    costtotal=25lw+ 150/w+150/l

    but l=5w
    costtotal= 125w^2+150/w+30/w

    take the derivative of cost.
    costtotal'=0=250w-150/w^2-30/w^2

    solve for w:

    250w^3-180=0
    w^3=180/250
    w= cubroot 7.2

    l= 4 cubroot 7.2

    h= 25/(lw)

    check my work.

  • CALC -

    moron

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