What are the decision variables

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Reference no: EM132243469

This is a practice problem for Mixed Integer Programming with a multi-part question (an explanation of the logic to derive the solution requested):

Problem 1 The curator at the Dallas Art Museum is planning a retrospective on C´ezanne. He has a choice of 100 paintings the museum already owns or can obtain on loan from other institutions. He has a budget B to spend on the exhibition. It cost bi to borrow painting i, i = 1,..., 100, for the exhibition. The curator wants to maximize the number of paintings in the exhibition subject to the budget constraint and additional constraints detailed below.

1: What are the decision variables?

2: What is the objective?

3: What is the budget constraint? Incorporate the following constraints in your formulation.

4: The curator wants to borrow at most 3 paintings from collector A, who owns paintings 1, 2, ..., 10.

5: If he selects painting 30, he must also select paintings 32 and 34.

6: If he selects painting 15 or 20, he must also select painting 25.

7: He must select as many paintings from curator B, who owns paintings 11, 12, ..., 19, as from curator C, who owns paintings 20, 17, ..., 29.

8: The paintings borrowed from curator D, who owns paintings 30, 31, ..., 39, can represent at most one third of the total paintings shown at the exhibition. 2

9: If 4 or more paintings are chosen among paintings 40 to 49, then painting 50 or 51 must be chosen as well.

10: Assume it is optimal to show paintings 1, 11, 21, 31, 41, 51 and 61. What constraint do you need to add to find the second-best solution?

Reference no: EM132243469

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