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Maximum Value of Functions

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A jewelry floor safe with a square base is to be made so as to have a total volume of 648 cubic inches. The side material for the safe costs $1 per square inch. The material for the top costs $4 per square inch while the material for the bottom costs $2 per square inch. What, in inches, would be the height of the most economical box which could be made given these conditions?

12 inches
15 inches
18 inches
21 inches
24 inches
27 inches
none of these

A hotel manager has 200 rooms available for rent each night. Experience shows that if she charges $40 per night, she will have full occupancy, but that for each $5 that she increases the price, 4 rooms become vacant. All other factors being equal, what will her maximum revenue be?

$16,820
$13,520
$8820
$12,000
$11,520
$18,000
none of these

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The maximum values of functions are found. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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