Question Details

MAT 540
WEEK 8
Susan Wong- Personal Budgeting Model
Susan Wong wants to develop a linear programming model for her budget to maximize her short-term investments during the year so she can take the money and reinvest it at the end of the year in a longer-term investment program.  
Susan has $3800 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	2750	July	3050
February	2860	August	2300
March	2335	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 1-month investments is 6% per year nominal (0.5%/month); on 3-month investments, the yield is 8% per year nominal (equivalent to 2% for 3 month); 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 year. At the end of the December, she would not invest the left over in short-term investments.  She would transfer the December left over to longer-term investment. 
There are two possible strategies to handle the matured short-term investments.  
I.	She uses the principal as part of her budget and transfer the interest earned to another long-term investment.  For example, if she has $100 left over in January that she invests for 3 month investment.  In April, when the investment matures, she uses the $100 she originally invested in her budget, but any interest on the $100 is invested elsewhere.    

a.	Based on this strategy, develop a linear programming model to determine how much she should put aside each month in short-term investments to maximize her short-term investment returns.  Solve the model.
b.	If she decides she doesn’t want to include all her original $3800 in her budget at the beginning of the year, but instead she wants to invest some of it directly in alternative longer-term investments, how much does she need to develop a feasible budge?
c.	If she decides to save money by cutting expenses, which month to cut expense would give her the best return?

II.	She use the entire matured short-term investment (i.e. principal plus the interest) as part of her budget. For example, if she has $100 left over in January that she invests for a 3 month investment.  In April, when the investment matures, she would use the $102 (principal plus interest) in her budget. 

a.	Based on this strategy, develop a linear programming model based on this strategy and solve the model.

III.	Which strategy is better for her?

There are two deliverables for this case study, a short writeup of the project and the spreadsheet showing your work.  
Writeup
Your writeup should introduce your solution to the project by describing the problem. Correctly identify what type of problem this is. For example, you should note if the problem is a maximization or minimization problem, as well as identify the resources that constrain the solution. Identify each variable and explain the criteria involved in setting up the model. This should be encapsulated in one (1) or two (2) succinct paragraphs.
After the introductory paragraph, write out (explain) the L.P. model for the problem, including the explanation of the objective function and all constraints. Then, you should present the optimal solution, based on your work in Excel. Explain what the results mean.
Finally, write a paragraph addressing the part of the problem pertaining to sensitivity analysis and shadow price.
Excel
As previously noted, please set up your problem in Excel and find the solution using Solver. Clearly label the cells in your spreadsheet. You will turn in the entire spreadsheet, showing the setup of the model, and the results.

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