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 X1, X2, X3, X4, X5, and X6 represent the six choices. For each of the following situations, write a constraint (or several constraints) that would be used.

(a) At least three 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 investment 6.

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

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