The Charm City Company is currently considering 4 proposals for investment. 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 three years.

                                                     Cash Requirements

Proposal         NPV          Year 1          Year 2                Year 3

     1                 8.5              4.10               3.00                    3.20

     2                 8.2              4.00               2.20                    1.80

     3                 9.1              3.80               3.10                    2.20

     4                 9.4              4.40               3.60                    2.80

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

(i) The total cash requirement cannot exceed 12.2 million dollars in the first year.

(ii) The total cash requirement cannot exceed 9.8 million dollars in the second year.

(iii) The total cash requirement cannot exceed 7 million dollars in the third year.

(iii) At most three of the proposals can be approved.

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

Formulate a capital budgeting integer programming problem by defining

(a) The decision variables.

(b) The objective function. What does it represent?

(c) All the constraints. What does each constraint represent?

Note: Do NOT solve the problem after formulating.