tank w/ rectangular base and sides and open at the top. width is 4m and volume is 36m^3. tank costs $10 per m^2 for the base and $5 per m^2 for the sides, what is the cost of the least expensive tank?

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The volume is LxWxH=36 Lx4xH=36 so L=36/4H we want the least surface area' Since the top is opened, the total surface area = area of the bottom=LxW+sum of areas of the 4 sides=2xLxH+2x4xH=2LH+8H plug in for L,2(36/4H)+8H=18/H+8H+4(36/4H)We want this to be minimum. find the first derivative, =0 ,find critical points Derivative WRT ,H The area A=8H+54/H dA/dH=8-54/H^2=0,solve for H and find the area and the amount