Question: A manager of a firm is currently reviewing a set of proposals prepared by her staff. The table below displays each proposal's net present value (NPV) in millions of dollars and each proposal's requirements for cash (in millions of dollars) for each of the next two years.

Cash Requirements

Proposal NPV Year 1 Year 2 Year 3

1 6.4 2.10 3.00 2.20

2 4.6 3.20 2.00 1.50

3 4.0 1.80 3.00 2.00

4 6.2 3.10 2.50 2.90

5 5.8 3.50 2.80 1.95

The manager wants to maximize the total NPV while meeting the following restrictions:

(i) The total cash requirement cannot exceed 10.5 million dollars in the first year.

(ii) The total cash requirement cannot exceed 8.2 million dollars in the second year.

(iii) The total cash requirement cannot exceed 8.8 million dollars in the third year.

(iv) At least three of the proposals must be approved.

(v) If proposal 2 is approved, then proposal 3 must also be approved.

Formulate a capital budgeting problem for the above situation, when the objective of the manager is to maximize the total NPV, by determining

(a) The decision variables.

(b) The objective function.

(c) All the constraints.

Note: Do NOT solve the problem after formulating.