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Innis Investments manages funds for a number of companies and wealthy clients. The investment strategy is tailored to each clients needs. For a new client, Innis has been authorized to invest up to $ 1.2 million in two investment funds: a stock fund and a money market fund. Each unit of the stock fund costs $50 and provides an annual rate of return of 10%; each unit of the money market fund costs $100 and provides an annual rate of return of 4%. The client wants to minimize risk subject to the requirement that the annual income from the investment be at least $60 000. According to Inniss risk measurement system, each unit invested in the stock fund has a risk index of 8, and each unit invested in the money market fund has a risk index of 3; the higher risk index associated with the stock fund indicates that it is the riskier investment. Inniss client also specified that at least $300 000 be invested in the money market fund. Determine how many units of each fund Innis should purchase for the client to minimize the total risk index for the portfolio.

S = units of stock funds.

M = units of money

Min RI = 8S + 3M

s.t.

50S

+

100M

1200000

Total BUDGET

5S

+

4M

60000

Expected RETURN

M

3,000

Min REQUIREMENT

S;M 0

The sensitivity report is shown in the figure below.

Objective function Value = 62000.000
		Variable		Value		Reduced Costs
		S		4000.000		0.000
		M		10000.000		0.000
		Constraint		Slack/Surplus		Dual Prices
		1		0.000		0.057
		2		0.000		- 2.167
		3		7000.000		0.000

Right Hand Side Ranges

		Constraint		Lower Limit		Current Value		Upper Limit
		1		780000.000		1200000.000		1500000.000
		2		48000.000		60000.000		102000.000
		3		No Lower Limit		3000.000		10000.000

Only Solve the following questions;

1. What is the optimal solution? Do not write zeroes as decimal places, do not write a comma between hundreds and thousands. Be concrete, it is not enough to copy 3 numbers from MS output.
2. Do values of 0; 0; 7000 represent slack or surplus? What is what? What is the interpretation of 7000. Be specific.
3. Will the optimal solution change if the objective function is changed to RI=8S+9M? Explain.
4. Will the optimal solution change if the objective function is changed to RI=6S+4M ? Explain.
5. Will the optimal solution change if the first constraint is changed to 50S+100M1 000 000? Explain.
6. Will the optimal solution change if constants on the right sides of constraints are changed to 1 000 000; 100 000; 6 000, respectively? Explain.
7. What will happen to the optimal value of RI (62 000) if total budget is increased by $1?
8. What is the interpretation of negative dual price of -2.167?
9. If following the optimal solution, how much return will she realize yearly?

Objective coefficient ranges Lower Limit Current Value Upper Limit Variable S 3.750 8.000 No upper Limit M No Lower Limit 3.000 6.400 Objective coefficient ranges Lower Limit Current Value Upper Limit Variable S 3.750 8.000 No upper Limit M No Lower Limit 3.000 6.400

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