Obviously H = 10, LW=1000, so L = 1000/W
C = 6*LW + 10*LW + 20*2*WH + 20*2*LH
C = 6000 + 10,000 + 400W + 400(1000/W)
C = 16,000 + 400W + 400,000/W
dC/dW = 400 - 400,000/W^2
max/min C is where dC/dW = 0
400W^2 = 400,000
W^2 = 1000
W = 31.62
L = 31.62
H = 10
A warehouse having a volume of 10,000 ft3 and a floor area of 1000 ft2 is to be built. The cost
of constructing the floor is $6.00/ft2, the cost of the roof is $10.00/ft2, and the cost of the walls
is $20.00/ft2. If W is the width, L the length, and H the height of the building, what should the
dimensions be such that the cost is minimal?
1 answer
1 answer