HELP!! OPTIMIZATION CALCULUS
posted by Kay .
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

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