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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. There are two possible strategies to handle the matured short-term investments. Develop an LP model for each strategy and answer the questions. Strategy I She uses the principal of the matured short-term investment as part of her budget and transfers the earned interest to another long-term investment. For example, she has put aside $100 in January for a 3-month investment. In April, when the investment matures, she receives $102 (principal plus interest). She uses the $100 she originally invested back to her budget for April, but $2 interest is invested elsewhere.