HELP!! OPTIMIZATION CALCULUS

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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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