Linear programming models are used by many Wall Street and Bay Street firms to select a desirable bond portfolio for their clients. The following is a simplified version of such a model. TAL Private Investments has $1 million to invest for a client and is considering an investment in four bonds. The expected annual return, the worst-case annual return and the duration of each bond are given below. (The duration of a bond is a measure of its sensitivity to interest rate changes.)

	Expected return	Worst-case return	Duration
Bond 1	10%	6%	7
Bond 2	8%	8%	4
Bond 3	11%	10%	7
Bond 4	14%	9%	9

TAL wants to maximize the expected return from the investment subject to three constraints that have been placed on it by the client:

1. The worst-case annual return of the portfolio should be at least 8%
2. The average duration of the portfolio must be no more than 7. (For example, a portfolio that was made up of $600,000 in Bond 1 and $400,000 in Bond 4 has an average duration of It may also help you to recognize that can be rewritten as or.)
3. At most, 45% of the portfolio can be in invested in a single bond.

Question #1 - Formulate a linear model that will help TAL make the portfolio composition decision. Be sure to define your decision variables clearly including the units of measure for each

Question #2 - Solve the problem using Excel and Solver and submit a printout of your model as is done in Question 4 above