The Texas Consolidated Electronics Company is contemplating a research and devel

Question

The Texas Consolidated Electronics Company is contemplating a research and development program encompassing eight research projects The company wants to maximize its profit. The company is constrained from embarking on all projects by the number of available management scientists (40) and the budget available for R&D; projects ($300,000). Further, if project 2 is selected, project 5 must also be selected (but not vice versa). Following are the resource requirements and the estimated profit for each project: Formulate an integer programming model for this problem.

Explanation / Answer

Let x1 = 1 if Project 1 is selected and = 0 if Project 1 is not selected.

Similarly, x2... x8 = 0 or 1 depending on whether the project is selected.

The integer programming model for this problem is as shown below:

Maximize Z = 0.36 x1 + 0.82 x2 + 0.29 x3 + 0.16 x4 + 0.56 x5 + 0.61 x6 + 0.48 x7 + 0.41 x8

Subject to

7x1 + 9x2 + 8x3 + 4x4 + 7x5 + 6x6 + 8x7 + 5x8 <= 40 (Constraint of scientists)

60x1 + 110x2 + 53x3 + 47x4 + 92x5 + 85x6 + 73x7 + 65x8 <= 300 (Constraint on budget)

x5 >= x2 (Constraint on project selection)

x1, x2, .... x8 = 0 or 1

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