We have some money available to invest for the next three years, and we consider the investment opportunities A, B and C :

Investment A : for each dollar invested now (beginning of year 1 ) , we receive $0.10 at at the end of the first year and $1.60 at the end of second y ear.

Investment B : for each dollar invested at the end of the first year, we will receive $1.60 at the end of second year

Investment C : for each dollar invested at the end of the second year, we will receive $1.20 at the end of the third year.

At any time, leftover cash may be invested in money market certificates, which pay 8% per year Right now, we have $100 000 available. We wish to invest at most $50 000 in any of the investments A, B, and C. We also wish to keep at least $20 000 in cash (i.e. in money market certificates) at any time. Formulate an LP that can be used to maximize cash on hand at the end of year 3. You will specify very clearly the decision variables , the objective function and the constraints.