Formulate a shortest path model to minimize the cost of meeting the demand for boxes. Box 1 2 3 4 5 6 7 Size 33 30 26 24 19 18 17 Demand 400 300 500 700 200 400 200 The unit cost (in dollars) of producing each box is equal to the box’s size
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Shortest path problem
A company sells seven types of boxes, ranging in size from 17 to 33 cubic feet. The demand and size of each box is given in the table below. The variable cost ($) of producing each box is equal to the box’s size. A fixed setup cost of $1000 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 a shortest path model to minimize the cost of meeting the demand for boxes.
Box 1 2 3 4 5 6 7
Size 33 30 26 24 19 18 17
Demand 400 300 500 700 200 400 200
The unit cost (in dollars) of producing each box is equal to the box’s size, for example, $24 per box of type 4 (with size 24). A fixed setup cost of $1000 is incurred to produce a particular size of boxes. For example, if you produce at least one box of type 5, there is a fixed setup cost of $1000, no matter how many boxes of type 5 to produce; the setup cost for type 5 is zero, if no boxes of type 5 are produced.
Only formulate the IP model
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