Quadz 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 binary (01) integer programming model is planned to help determine which of the six opportunities to choose. Variables A, B, C, D, E and F represent the six choices.

For each of the following situations, formulate a constraint that would be used:

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

(b) Either investment A or investment D must be undertaken, but not both.

(c) If investment D is selected, then investment F must also be selected.

(d) Investments D, E and F must be selected.

(e) Investment E must be selected if both investments B and C are also selected.

(f) Investment E cannot be selected unless both investments B and C are also selected