Consider the following nancial planning problem. Suppose that you start the year with $3,800 in cash, and your expected liabilities throughout the...

Every time one of your short-term investments matures, you will use the principal as

part of your budget (i.e., you will continue investing it and using it for expenses), but

you transfer any interest earned to another long-term account, which is not available

for your budgeting process. (For example, if you invest $100 in 3-month securities at

the beginning of January, you get back $102 at the beginning of April; the principal of

$100 can be reinvested, but the yield of $2 is transferred to the other account. Thus,

the interest is not compounded over the course of the year.)

You do not want to conne yourself to investments that will all mature by the end

of the year. Every type of investment is available in every month, even if it does not

mature until the following year: in that case, the return still counts for your objective,

but you won't be able to use the principal again for the rest of the year. For simplicity,

suppose that the full return is always counted toward the objective, e.g., a 7-month

investment made in December is still treated as earning 12% per year.

Now, do the following:

a) Formulate, and solve in Excel, a linear programming model that will help you meet

your monthly obligations while maximizing your total investment return through the

entire year.

b) What is the minimum amount of starting capital that you need to meet your monthly

obligations? (Hint: use the sensitivity report.)

c) In a Word document, formulate the dual LP of the problem in part a) and give an

economic interpretation.