1. As a financial consultant, Mary (one of your clients) requires your assistance in how to pay off her debts owed to three credit-card companies, as detailed in the next table.

Credit-Card Company

A B C

Balance ($)

20,000 50,000 30,000

Monthly Interest Rate (%)

1.5 1 0.5

Mary has to pay off within 24 months and can repay at most $5000 per month. Her goal is to minimize the total payment. For example, if she repays $1000 to Company A at the end of month 1, her outstanding debt will be $19,300 = $20,000(1 + 1.5%) - $1000.

You assist Mary in attaining her goal by doing the next three steps:

(a) Formulate a linear program by clearly stating the decision variables, the objective function and constraints. [10 marks]

(b) Develop an Excel worksheet for the linear program in (a) and solve it using Solver. [7 marks] (c) From the answer report in (b), explain the optimal plan of payments with logical reasoning.

[5 marks]