Question 1095519: a monkey cage with a square base and rectangular sides is to be constructed. the volume of the cage must be 300 cubic feet. the cost per square foot of the top is $8, the cost per square foot of the bottom is $4, and the cost per square foot of each of the wall is $15. let the height of the cage be h and the length of one of the bases be l. express h in terms of l. then express the total cost of the money cage in term of l
Found 2 solutions by Boreal, josmiceli:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! The base has side L, so the area of the base is L^2
since the top is the same as the base, that area is also L^2, and the two ends have area 2L^2.
The height is H and the width of that rectangle is also L, since it has to match the base.
Therefore, the 4 sides each of area HL are 4HL
The total area is 4HL+2L^2=A
The cost for the base is $4 per square foot, so that is $4L^2 for the base and $8L^2 for the top.
The cost of the wall per square foot is $15 so $60HL is the total cost of the walls.
The total cost of the box is A=$12L^2+$60HL.
The volume is L^2*H=300, so H=300/L^2
Substitute into the total cost to get $12L^2+$60*L*300/L^2=$12L^2+$18000/L.
Check
Suppose L is 10 and H=3, so V=300
Base has area 100 sq units and each wall has area 30, so total area of wall is 120.
The cost of the base is $400 and the top is $800; each wall is $450, so the total is $3000.
12L^2+18000/L=1200+18000/10=$3000.
Answer by josmiceli(19441)  (Show Source):
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