Trapeze Investments is a venture capital firm that is currently evaluating six d

Question

Trapeze Investments is a venture capital firm that is currently evaluating six different investment opportunities. There is not sufficient capital to invest in all of these, but more than one will be selected. A 0–1 integer programming model is planned to help determine which of the six opportunities to choose. Variables represent the six choices. For each of the following situations, write a constraint (or several constraints) that would be used

.(a) At least 3 of these choices are to be selected.

(b) Either investment 1 or investment 4 must be undertaken, but not both.

(c) If investment 4 is selected, then investment 6 must also be selected. However, if investment 4 is not selected, it is still possible to select number 6.

(d) Investment 5 cannot be selected unless both investments 2 and 3 are also selected.

(e) Investment 5 must be selected if both investments 2 and 3 are also selected.

Explanation / Answer

Let Xi be the binary variable which represent the six choices of investment opportunities. Constraints representing the restrictions are following:

(a) X1+X2+X3 >= 3

(b) X1+X4 = 1

(c) X6 >= X4

(d) X2+X3 >= 2X5

(e) X2+X3 - 2X5 <= 1

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