SOLUTION: You have been asked to design a rectangular box with a square base and lid. The volume of the box must be 12 m3. The cost per square meter of material for the base is $0.50, for th
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Question 1035166: You have been asked to design a rectangular box with a square base and lid. The volume of the box must be 12 m3. The cost per square meter of material for the base is $0.50, for the sides $0.20, and for the lid $0.10. If the total cost of materials is a minimum, then the dimensions (in meters) of the box are
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The volume of the box must be 12 m3.
The cost per square meter of material for the base is $0.50, for the sides $0.20, and for the lid $0.10.
If the total cost of materials is a minimum, then the dimensions (in meters) of the box are
:
let x = the side of the square base
then
x^2 = the area of the base and the lid
and the volume is to be 12 cu/m. therefore:
12/x^2 = height of the box
:
Cost = base area + side areas + lid area
C = .5x^2 + .2(4*x*) + .1x^2
cancel x
C = .6x^2 + .2(4*)
C = .6x^2 +
Graphically, we can see minimum cost occurs when x = 2
The dimensions
L=2;
W=2
H = 12/2^2 = 3 m
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