SOLUTION: A rectangular box is to have a square base and a volume of 40 ft3. If the material for the base costs $0.35/ft2, the material for the sides costs $0.05/ft2, and the material for th
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Question 1028760: A rectangular box is to have a square base and a volume of 40 ft3. If the material for the base costs $0.35/ft2, the material for the sides costs $0.05/ft2, and the material for the top costs $0.15/ft2, determine the dimensions of the box that can be constructed at minimum cost.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A rectangular box is to have a square base and a volume of 40 ft3.
If the material for the base costs $0.35/ft2, the material for the sides costs $0.05/ft2, and the material for the top costs $0.15/ft2, determine the dimensions of the box that can be constructed at minimum cost.
:
let x = the length of the side of the square base
then
= the height of the box
:
Area of the top and bottom will be x^2
Area of each of the 4 sides will be :
simplifies to
Fours sides area: 4* =
:
The cost equation
Cost = base cost + side cost + top cost
C(x) =
C(x) =
Graph this equation to find the min cost
minimum cots occurs when x = 1.7 ft, the length and width of the box
Find the height
h =
h = 13.8 ft
:
The box dimension for min cost: 1.7 by 1.7 by 13.8
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