SOLUTION: A closed box with square base is to be built to house an ant colony. The bottom of the box and all four sides are to be made of material costing $2/ft2, and the top is to be constr
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Question 1075632: A closed box with square base is to be built to house an ant colony. The bottom of the box and all four sides are to be made of material costing $2/ft2, and the top is to be constructed of glass costing $4/ft2. What are the dimensions of the box of greatest volume that can be constructed for $72? (Enter the dimensions (in feet) as a comma separated list.)
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let each of the 2 base dimensions =
Let the height dimension =
The area of the 4 sides =
The area of the base =
The area of the top is also
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The volume is:
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If volume is maximized, then the cost of
construction will still be $72 total.
I will assume that this is a calculus problem, and
I will set the slope of equal to zero.
slope =
and
The dimensions in feet are:
2,2,3
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check answer:
Here's the plot of volume, , on vertical axis
and base dimension, , on the horizontal axis.
It looks like is maximized when
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Get a 2nd opinion if needed
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