A company sells seven types of boxes, ranging in volume from 17 to 33 cubic feet. The demand and size of each box is given in Table 7. The variable cost (in dollars) of producing each box is equal to the box's volume. A fixed cost of $1,000 is incurred to produce any of a particular box. If the company desires, demand for a box may be satisfied by a box of larger size Formulate and solve a shortest-path problem whose solution will minimize the cost of meeting the demand for boxes.

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Box 2 3 4 5 6 Size 33 30 26 24 19 18 17 Demand 400 300 500 700 200 400 200