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This is problem 16 Section 4.6 page 246.

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 dollar/sq ft, and the top is to be constructed of glass costing dollar/sq ft. What are the dimensions of the box of greatest volume that can be constructed for dollars?

NOTE: Let denote the length of the side of the base and denote the height of the box.

  • calculus -

    some actual numbers would make this easier to answer. . . Not everyone has access to your text -- Or even knows which text that is . . .

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