Your job is to design a closed rectangular box of minimum cost. Suppose the box is to be of volume cubic cm; and the cost of material for the front and backsides is b dollars per square cm, c dollars per square cm for the left and right two sides, and d dollars per square cm for the top and bottom sides.

Question

Your job is to design a closed rectangular box of minimum cost.  Suppose the box is to be of volume   cubic cm; and the cost of material for the front and backsides is b dollars per square cm, c dollars per square cm for the left and right two sides, and d dollars per square cm for the top and bottom sides.

anonymous · Answer

volume = lwh 
area of 1 side = lw
cost of front and back = blw
cost of left and right = clw
cost of top and bottom = dlw

total cost = blw + clw + dlw
find the derivative and set it to 0.