midtermIE5112

# Draw the corresponding network representation you may

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the cost of the assignments. Draw the corresponding network representation. You may formulate the problem (and thus the corresponding network) as either a transportation problem or an assignment problem (your choice). Job 1 2 3 4 5 Contractor 1 8 6 5 7 4 2 6 5 3 2 3 7 8 5 6 3

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6. (16 pts) A greenhouse operator plans to bid for the job of providing flowers to city parks. She will use tulips, daffodils, and flowering shrubs in three types of layouts. A type one layout uses 30 tulips, 20 daffodils, and 4 shrubs. A type two layout uses 10 tulips, 40 daffodils, and 3 shrubs. A type three layout uses 20 tulips, 50 daffodils, and 2 shrubs. The net profit is \$50 for each type one layout, \$30 for each type two layout, and \$60 for each type three layout. The greenhouse operator’s current inventory consists of 1000 tulips, 800 daffodils, and 100 flowering shrubs. She would like to know how many layouts of each type should be used in order to maximize total profit. Figures 1 and 2 show the AMPL model and session to solve this problem. Use the information from these two figures to answer the following questions. Note that this is a linear programming problem, so we are assuming that the greenhouse operator may sell a fraction of a layout. Also, provide brief reasons for your answers, not just “yes” or ”no”. (One sentence should be sufficient.) (a) In the optimal solution, which type (or types) of flower has (have) unused inventory? (b) Suppose that the profit for layout type two is increased from \$30 to \$55. Will the optimal solution change?
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