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March 30, 2017

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A rectangular storage container with a lid is to have a volume of 8 m. The length of its base is twice the width. Material for the base costs $4 per m. Material for the sides and lid costs $8 per m. Find the dimensions of the container which will minimize cost and the minimum cost.

base width = m

base length = m

height = m

  • HELP!! OPTIMIZATION CALCULUS - ,

    This is pretty easy.

    area sides=2L*m+2Wm
    area bottom= LW
    area lid= LW

    Volume=lwm
    But l=2w
    volume=2w^2 m
    or m= 4/w^2

    costfunction= 4*basearea+8(toparea+sides)


    Now, write that cost function in terms of w (substitute)
    take the derivatative. with respect to w, set to zero,and solve for w, then use your relations to get l, and h.

  • HELP!! OPTIMIZATION CALCULUS - ,

    i get a derivcative of 24w^2+24w^-1
    is that correct?

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