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Model+Programming+Problems

Model+Programming+Problems - i Exp Expense on project i...

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4. The Texas Consolidated Electronics Company is contemplating a research and development program encompassing eight research projects. 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). Formulate the integer programming model for this problem, and solve it by using the computer. First we introduce notations: Decision variables: : i x = 1 if project i is selected , 0 otherwise, i=1,2,…,8 Parameters:
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Unformatted text preview: i Exp : Expense on project i, i=1,2,…,8 (2 nd column in the table) i Num : Number of scientists required on project i, i=1,2,…,8 (3 rd column in the table) i P : Profit on project i, i=1,2,…,8 (4 th column in the table) IP model Max ∑ = 8 1 i i i x P s.t. 300000 * 8 1 ≤ ∑ = i i i x Exp (budget constraint) 40 * 8 1 ≤ ∑ = i i i x Num (budget constraint) (if project 2 is selected, project 5 must also be selected ,but not vice versa). i x binary, i=1,2,…,8 Optimal solution: We select project 2,5, and 6, with the maximum profit of $ 1,990,000.00 . 5 2 x x ≤...
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