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 2 years ago
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 1 dollar/sq ft, and the top is to be constructed of glass costing 5 dollar/sq ft. What are the dimensions of the box of greatest volume that can be constructed for 72 dollars?
NOTE: Let denote the length of the side of the base and denote the height of the box
 2 years ago
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 1 dollar/sq ft, and the top is to be constructed of glass costing 5 dollar/sq ft. What are the dimensions of the box of greatest volume that can be constructed for 72 dollars? NOTE: Let denote the length of the side of the base and denote the height of the box

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m.auld64
 2 years ago
Best ResponseYou've already chosen the best response.0i know how to do this but im having trouble coming to the correct answer

kumar2006
 2 years ago
Best ResponseYou've already chosen the best response.1V = x^2 y ....... x = base we also know that 72 = 5(x^2) + 4(xy) + x^2 72 = 6x^2 + 4xy xy = (36  3x^2)/2 thus V = x(36  3x^2)/2 get the derivative and set it to zero, the resulting xvalue is the length of the base of the box with the greatest volume.

m.auld64
 2 years ago
Best ResponseYou've already chosen the best response.0can you help me do that cuz im apparently not doing it right

Chlorophyll
 2 years ago
Best ResponseYou've already chosen the best response.0Surface Area = 2 tops + 4 sides Area of square = 2 * x² + 4 * xy Total Cost: $5 *x² + $1* ( 4xy + x²) = $ 72 6 x² + 4xy = 72 =>Area: xy = (72  6x² ) / 4 = 18  1.5 x² => Volume: x ( xy) = 18x  1.5 x³ Thus maximum Volume: V' = 18  4.5 x² = 0 => x = 2 ft, y = 6 ft
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