a rectangular box with a volume of 784 cubic feet is to be constructed witha square base and top. The cost per square foot for the bottom is 15 cents, for the top is 10 cents, and for the sides is 2.5 cents. What will minimize the cost?

I am in an AP calc class but have been sick for the last few classes and this was our homework. I dont want to come in empty handed and would really like some help getting through this.

Question

a rectangular box with a volume of 784 cubic feet is to be constructed witha  square base and top. The cost per square foot for the bottom is 15 cents, for the top is 10 cents, and for the sides is 2.5 cents. What will minimize the cost?

I am in an AP calc class but have been sick for the last few classes and this was our homework. I dont want to come in empty handed and would really like some help getting through this.

tkhunny · Answer

Rule #1 -- Name Stuff.

Base = B
Height = H

Volume = H*B*B = 784

Your task is to find the WEIGHTED surface area.

anonymous · Answer

Let x is the side of the square, y is the height
->         V =     x²  y   =   784 ft³
          SA =     2 bottoms     +  4 sides
->Cost C =    15x²  + 10x²   + 4 * 2.5 x  * 784 /x² 
                =     25x²   + 784 / x
Minimum Cost when C' = 0
@irawrd Hopefully I give you sufficient boost  :)