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Minimization Word Problems

Example 1:

A rectangular warehouse is to have 5000 square feet of floor area and is to be divided into two rectangular rooms by an interior wall. Cost per running foot is $125 for exterior walls and $250 for the interior wall.


a. What dimensions will minimize total wall cost?


b. What is the minimum cost ?


Example 2:

A cylinder storage tank is to contain V=128,000π cubic feet. The cost of the tank is proportional to its area, so the minimal-cost tank will be the one with minimum area. The volume (V) of a cylinder of radius r and height h is πr^2h. Its surface area of the area of top and bottom, 2πr^2, plus the side area 2πrh.


a. Find the dimensions, r and h, of the

minimal-area tank