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March 29, 2017

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CarpetPlus sells and installs floor covering for commercial buildings. A CarpetPlus account executive, was just awarded the contract for five jobs. This executive now must assign a CarpetPlus installation crew to each of the five jobs. Because the commission, the executive will earn depends on the profit CarpetPlus makes, This executive would like to determine an assignment that will minimize total installation costs. Currently, five installation crews are available for assignment. Each crew is identified by a color code, which aids in tracking of job progress on a large white board. The following table shows the costs (in hundreds of dollars) for each crew to complete each of the five jobs.

Crew 1 2 3 4 5
Red 30 44 38 47 31
White 25 32 45 44 25
Blue 23 40 37 39 29
Green 26 38 37 45 28
Brown 26 34 44 43 28

(a) Develop a network representation of the problem.

(b) Formulate and solve a linear programming model to determine the minimum cost assignment.

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