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an integer programming model that minimizes the total cost

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Consider a capital budgeting problem with 5 projects from which to select. Let Xi = 1 if project i is selected, 0 if
not, for i = 1, 2, 3, 4, 5. Projects cost $100, $200, $150, $75, and $300 respectively. The decision-maker must
choose no fewer than 3 projects, and if project 3 is chosen, then project 4 must also be chosen. Furthermore,
projects 1 and 5 can not be chosen together.

(a) Write an integer programming model that minimizes the total cost.
(b) Write the above model in standard form.
(c) Solve the problem using a computer. Explain the solutions clearly.

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An integer programming model that minimizes the total cost is presented.

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