LINEAR PROGRAMMING FORMULATION Bert Humphries has left his home in a small town

Question

LINEAR PROGRAMMING FORMULATION

Bert Humphries has left his home in a small town in rural manitoba and moved to toronto to enroll in a 4-year undergraduate program in economics. Bert is planning an investment strategy for the 4-year period, with the goal of having the largest possible amount of cash on hand when he graduates. Bert has some revenue from a combination of an RESP fund that his parents opened for him when he was a baby, scholarship funds, and a small inheritance he recently received from his grandmother. His estimate of revenues and expenses over the four years is shown in the following table. Bert has $5000 in cash at the begining of the 1st year.

Year Revenues Expenses

2009-2010 $30,000 $10,000

2010-2011 $40,000 $25,000

2011-2012 $25,000 $25,000

2012-2013 $15,000 $12,500

Any money left over at the end of a year can be invested in guaranteed investment certificates (GICs) for one year at an annual interest rate of 2.9%, for two years at 3.0%, for 3 years at 3.1%, or for 4 years at 3.4%. Bert uses the following rule for each of the 4 years:

Money invested + Expenses paid < (less than or equal to) Revenues + Money earned from investment

(a) Formulate a linear program to determine an investment strategy that will maximize the value of Bert's GICs at the end of the 4th yr. (Hint: Bert can have up to 4 GICs coming due at the end of the 4th yr: a 4 year GIC invested at the begining of year 1, a three-year GIC invested at the begining of year 2, a two-year GIC invested at the begining of year 3, and a one year GIC invested at the begining of year 4. It is the sum of these values that Bert wants to maximize, as he plans to cash in all of his GICs and travel the world for a year between graduation and starting his career.)

b) Solve using excel

Explanation / Answer

Let us assume Investment made in 4 yeras - I1, I2, I3, I4

Obj. Function is Max Value at the end 4th year = Maximize (Cumulative Interest earned + Invested Money each Year)

Maximum Value at the end of 4th year = 90342

year 1 2 3 4 Renenue -R 30000 40000 25000 15000 Expenses -E 10000 25000 25000 12500 Changing Cells I1 I2 I3 I4 Invevest -I 5000 15620 450 -1.10134E-13 Interest Rate -IR 3.4 3.1 3 2.9 Interest earn-IE 170 620 450 0 Max Investment 5000 20000 15000 0 Constraints 15000 <= 30170 40620 <= 40620 25450 <= 25450 12500 <= 15000 5000 <= 5000 15620 <= 20000 450 <= 15000 -1.1E-13 <= 0 Obj. Fun 90342

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