Lewis (1996). Monthly bills in a household are received monthly (e.g., utilities and home mortgage), quarterly (e.g., estimated tax payments), semiannually (e.g., insurance), or annually (e.g., subscription renewals and dues). The following table provides the monthly bills for next year.

To account for these expenses, the family sets aside $1000 per month, which is the average of the total divided by 12 months. If the money is deposited in a regular savings account, it can earn 4% annual interest, provided it stays in the account at least 1 month. The bank also offers 3-month and 6-month certificates of deposit that can earn 5.5% and 7% annual interest, respectively. Develop a 12-month investment schedule that will maximize the family’s total return for the year. State any assumptions or requirements needed to reach a feasible solution. Solve the model using Solver of AMPL.

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Month Jan. Feb. Mar. Apr. May June July $ 800 1200 400 700 Total Aug. Sep. Aug. Sep. Oct. Nov. Dec. 1100 1300 1600 12,000 600 900 1500 1000 900