# How can I formulate the Linear Programming problem below? [on hold]

I and some friends are having trouble formulating the linear programming problem below. Itâ€™s part of a Operations Research course. When I talk about formulate, Iâ€™m talking about Decision Variables, Objective Function, Constraints, Sign Restrictions.

Iâ€™m sorry if the text is too big but thatâ€™s the only way I found to put the problem here.

Mr. Jones is seeking for an investment plan for the next six years. Currently, he has two million euro available for investment. Moreover, at the end of each of the next six years he expects the following income stream, given in thousand euro, from previous investments: 600, 500, 450, 380, 350 and 320.

Mr. Jones was told that the company Alpha is seeking for partners to participate on some development projects. Currently, Alpha is running three development projects: P1, P2, and P3. According to the manager of Alpha, one that fully participates can expect the following cash flow stream, given in thousand euro, at the beginning of each of the next six years (negative numbers represent investments and positive numbers represent income):

Year 1 2 3 4 5 6 7

P1—> -3000 (Y1), -1000 (Y2), -1800 (Y3), 400 (Y4), 1800 (Y5), 1800 (Y6), 5500 (Y7)
P2—> -2000 (Y1), -500 (Y2), 1500 (Y3), 1500 (Y4), 1500 (Y5), 200 (Y6), 1000 (Y7)
P3—> -2000 (Y1), -2000 (Y2), -1800 (Y3), 1000 (Y4), 1000 (Y5), 1000 (Y6), 6000 (Y7)

As remarked by the manager, the cash flow is proportional to the percentage of investment. Moreover, the decision about participating, or not, on a given project must be made at the beginning of the six year period.

Mr. Jones knows that there is no point on leaving money apart on the bank. Thus, if applied, he may also invest in surplus funds at 1.5 percent net interest per year.

Knowing that Mr. Jones may borrow money for twelve month intervals at 1.75 percent net interest per year, but that 2 million euro at most can be borrowed at one time, what would be the investment plan that maximizes the accumulated capital at the end of the six years?

Question- Formulate in Linear Programming such that the best investment plan is determined.

There are other questions, but this the one I would like to understand 🙂

I tried different ways of solving this problem, but all of them are missing something. The dividends, the different amount of investment on the first years on each project, the income stream and the possibly of puttinh money on the bank and also borrow money, are all confusing me. I did various problems but this one is really different of I’ve done.

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