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 (dollar 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

Considered below ways of selecting projects keeping the maximum budget of $300000 in view

CASE 1 : If project 2 is selected, estimated cost of project 2 & 5 = 110000+92000 = 202000. Number of scientists required = 9 +7 = 16.

So balance budget left = 300000- 202000 = 98000 and balance scientists avaialble = 40-16= 24

if project 2 and project 5 selected, then there is only one project i.e.6 is selected keeping the maximum of budget 300000 $ in view and maximum profit .

CASE2: selected the projects with cost in ascending order keeping the maximum budget of 300000 $

CASE 3 : Considered the projects without project 2 and cost value nearing to 300000 $ and project with maximum profit

Case 1 is seams to be good with maximum profit.

Project Expense in 1000s $ Scientists required Estimated profit in 1000000s $ Cost in $ EstimatedProfit 1 60 7 0.36 60000 360000 2 110 9 0.82 110000 820000 3 53 8 0.29 53000 290000 4 47 4 0.16 47000 160000 5 92 7 0.56 92000 560000 6 85 6 0.61 85000 610000 7 73 8 0.48 73000 480000 8 65 5 0.41 65000 410000

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