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How do I solve this optimization problem?
A manufacturer wants to design an open box with a square base and a surface area of 108 square inches. What dimensions will maximize the volume of the box?
I understand how to solve using the calculator I just need some help finding the two equations to use.
The square base would tell me l=w, and V=l x w x h so we can make Volume=L^2h=Max
What is the second equation involving surface area?
Thanks in advance :)
1 Answer
- 8 years agoFavorite Answer
S.A. = area of square base + area of sides
108 = l^2 + 4lh
h= (108 - l^2)/(4l)
Volume = lwh = l^2h
V = l^2((108 - l^2)/(4l))
For max volume, l = 6 inches
w = l = 6 inches
h = (108 - 6^2)/(4*6) = 3 inches
For a max volume of 108 inches^3
I think Tom has made an error in writing the S.A. equation, it should be over 4l.
Gl
