John is considering a 5 year investment plan using $2200. At the beginning of ea

Question

John is considering a 5 year investment plan using $2200. At the beginning of each year, he can invest money in one or two year time deposits. The bank pays 8% interest on one year deposit and 17% total on two year deposits. In addition, starting at the beginning of the second year, the bank will be offering 3 year certificates with a total return of 27%. If John invests his money every year, formulate an LP that will determine the investment strategy for maximum profit. There is a penalty attache to early withdrawal, so John will not consider any investment that mature beyond the 5th year.

Explanation / Answer

Let xi be the investment done in one year time deposits in year i , i in 1,2,3,4,5 Let yi be the investment done in two year time deposits in year i, i in 1,2,3,4 Let zi be the investment done in 3 year certificates in year i, i in 2,3 The problem is really a kind of inventory problem. In a given year the amount of money carried forward from the previous year plus the profit from deposits and certificates.one important note here is Inventory grows while in storage in this case but in real inventory problems, stock often decreases due to spoilage. Let P be the final investment value when all the investments are cashed at the end of fifth year Maximize (P - 2200) subject to the following constraints first year, x1 + y1 = 2200 second year, x2 + y2 + z2 = 1.08 x1 third year, x3 + y3 + z3 = 1.08x2 + 1.17y1 fourth year, x4 + y4 = 1.08 x3 + 1.17y2 fifth year, x5 = 1.08x4 + 1.17y3 + 1.27z2 Final Investment Value, P = 1.08x5 + 1.17y4 + 1.2z3 xi,yi,zi >=0

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