Assignment:
Q: Susan Wong wants to develop a linear programming model for her budget. The objective is to maximize her short-term investments during the year so she can take the money and reinvest at the end of the year in a longer-term investment program.
Susan has $3000 in her bank account at the beginning of this year. Her after-taxes-and-benefits salary is $29400 per year which she receives in 12 equal monthly paychecks ($2450/month) at the end of each month. Susan has computed her expected monthly liabilities for this year, as shown in the following table.
|
Month
|
Bills ($)
|
Month
|
Bills ($)
|
|
January
|
2860
|
July
|
3050
|
|
February
|
2750
|
August
|
2300
|
|
March
|
2550
|
September
|
1975
|
|
April
|
2120
|
October
|
1670
|
|
May
|
1205
|
November
|
2710
|
|
June
|
1600
|
December
|
2980
|
Susan has decided that she will invest any money she doesn't use to meet her liability each month in either 1-month, 3-month or 7-month short-term investment vehicles. The yield on a 1-month investment is 6% per year nominal (0.5%/month). The yield on a 3-month investment is 8% per year nominal (equivalent to 2% for 3 months). On a 7-month investment, the yield is 12% per year nominal.
These are the assumptions for the linear programming model. All her bills come due at the end of the month. She receives her monthly salary at the end of the month. She puts aside money for short-term investments at the end of the month. She does not have to confine herself to short-term investments that will all mature by the end of the year. At the end of the December, she would not invest the balance in short-term investments. She would transfer the December balance to longer-term investment.