Betty and Bob Box Company makes open-topped boxes as per figure below. The volume of the...

 

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Betty and Bob Box Company makes open-topped boxes as per figure below. The volume of the box is 200 cubic feet. The bottom of the box is a square and costs $14 per square foot. The rectangular sides cost $4 per square foot. Using methods of calculus find the dimensions of the box (find x and h) that minimize the cost. What is the minimum cost of the box? Be sure to justify the existence of your minimum by rules of the calculus. оpen h Betty and Bob Box Company makes open-topped boxes as per figure below. The volume of the box is 200 cubic feet. The bottom of the box is a square and costs $14 per square foot. The rectangular sides cost $4 per square foot. Using methods of calculus find the dimensions of the box (find x and h) that minimize the cost. What is the minimum cost of the box? Be sure to justify the existence of your minimum by rules of the calculus. оpen h