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Ft. Wa 12 10 100 100 100 St. Louis Evansville 10 Demand 150 60 45 45 OPTIMAL TRANSPORTATION SCHEDULE 09494044 SHIP FROMTO DESTINATION ORIGIN 0 10 45 4 100 0 0 0 50 50 00 1) 1755 2) 1557 3) 1575 0
Tower Engineering Corporation is considering undertaking six proposed projects for the next fiscal year. The company must: Use no more than 175 engineers; Use no more than 150 support personnel; If either project 6 or project 4 is done, both must be done; Project 2 can be done only if project 1 is done; If project 5 is done, project 3 must not be done and vice versa; No more than three projects are to be done. The projects, the number of engineers and the number of support personnel required for each project, and the expected profits for each project are summarized in the following table: Project Engineers Required Support Personnel Required Profit ($1,000,000s) 20 55 47 38 90 63 15 45 50 40 70 70 1.0 1.8 2.0 1.5 3.6 2.2 Let Pi 1 if project i is chosen,0 otherwise. If this problem is formulated as a binary integer program, the objective function should be: 1) Max:P1 +1.8P2+2P3 +1.5P4+3.6P5+2.2P6 2) Max:20P1+ 55P2 + 47P3 +38P4+90P5+63P6 3) Min:15P1 + 45P2 +50P3 + 40P4 +70P5 +70P6
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Answer #1

Multiply the optimum solution with the costs. The objective function value will be

100*5 + 50*3 + 10*6 + 50*2 + 45*12 + 45*9 = 1755

This is a profit maximization problem. Engineers and support personnel are constraints. Thus the objective function will be.

Max P1 + 1.8P2 + 2P3 + 1.5P4 +3.6P5 + 2.2P6

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