Your grandfather has just left you $1 million. You plan to invest this money in
ID: 3008071 • Letter: Y
Question
Your grandfather has just left you $1 million. You plan to invest this money in four investments stocks,bonds, and real estate. Investments in stocks and bonds are available at the begining of each of the next 6 years. Each dollar invested in stocks at the begining of the year returns an average of $1.20 (a profit of .20) in time for immediate reinvestment 2 years later. Each dollar invested in bonds at the begining of each your returns $1.40 three years later for reinvestment.
In addition, money making investments in savings in a credit union and in real estate are available at the begining each year. Each dollar invested in the credit union at the begining of each year returns $1.10 one year later. Each dollar invested in real estate at the begining of a year returns $1.30 two years later.
You would like to diversify your investments in order to minimize risk. The total amount invested in stocks should not exceed 30% of the total investment in the other alternatives. Furthermore, you want to invest at 25% of the total investment in the credit union savings plan. You are planning to get married at the end of the third year, and want to make sure that the amount of cash you will have at that time (to show off your bride, but not to spend) will be at least $150,000.
If you are attempting to maximize the amount of money (cash) you will leave at the end of the sixth year, how would you formulate a linear programming model?
Explanation / Answer
B, C, R, and S are the investments of 1st year in their respective categories.
Objective Function:
Max Z = 1.4*1.4*B + 1.1*1.1*1.1*1.1*1.1*C + 1.3*1.3*1.3*R + 1.2*1.2*1.2*S (Return at the end of 6th Year)
Solving the above Linear programming using Excel Solver we get:
2,050,378
(Objective Function)
Overall Investment 1,000,000 Options Returns Duration of Investment Decisio Variables Bonds 1.4 3 B Credits 1.1 1 C Real Estate 1.3 2 R Stocks 1.2 2 SRelated Questions
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