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.