Question

Assignment I: Assume you have $50,000 to invest over the next five years. At the beginning of each year you can invest the available money in one, two or three-year time deposits. The bank pays 1.1% interest on one-year deposits, 2.1% interest (total) on two-year time deposits, and 3.2% interest (total) on three-year deposits. For instance, if you invest $1000 at the beginning of year 1 in one-year deposits, your return at the end of year 1, or beginning of year 2, would be 1.01 1000-$1010. This amount ($1010) wll be invested at the beginning of year 2. If you invest the money that is available at the beginning of every year, formulate a linear programming to maximize your total cash on hand at the end of the fifth year A: Assume that you can invest at the beginning of each year any value in the available your linear programming model. (6 marks) B: Solve your investment LP model using Excel-Solver and obtain the optimal solution.

Answer 1

A)

A11 Amount invested for 1 year in 1 year

A12 Amount invested for 2 year in 1 year

A13 Amount invested for 3 year in 1 year

A21 Amount invested for 1 year in 2 year

A22 Amount invested for 2 year in 2 year

A23 Amount invested for 3 year in 2 year

A31 Amount invested for 1 year in 3 year

A32 Amount invested for 2 year in 3 year

A33 Amount invested for 3 year in 3 year

A41 Amount invested for 1 year in 4 year

A42 Amount invested for 2 year in 4 year

A51 Amount invested for 1 year in 5 year

Total amount, T = A33*(1+1.1%)^3+A42*(1+2.1%)^2+A51*(1+3.1%)

Objective is Max T subject to

Constraints

A11 + A12 + A13 <= 50000

A21+A22+A23<= A11*1.011

A31+A32+A33<= A21*1.011+A12*1.021^2

A41+A42<= A13*1.031^3+A22*1.021^2+A31*1.011

A51<= A41*1.011