1. Foundreiz, a foundry company has funds to the tune of AED 100 million that can be allocated to projects A, B, C, D, and E. The net cash flows associated with an investment of AED 1 in each project are provided in the table below. Note that time 0 = present time, time 1 = 1 year from now, time 2 = 2 years from now, and time 3 = 3 years from now. For example, AED 1 invested in investment B requires AED 1 cash outflow at time 1 and returns AED 0.5 at time 2 and AED 1 at time 3. To ensure that the firm remains reasonably diversified, the firm will not commit an investment exceeding AED 75 million for any project. The firm cannot borrow funds and therefore, the cash available for investment at any time is limited to the cash in hand. The firm will earn interest at 8% per annum by parking the un-invested funds in money market investments.
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3. Assume that the returns from investments can be immediately re-invested. For example, the positive cash flow received from project C at time 1 can immediately be re-invested in project B. Formulate this problem as an LP model (linear programming) so as to maximize cash on hand at time 3.