1. Suppose the following LPP together with its formulation and MS output

Note! – Calculations must be done on word, every step must  be shown. 

complete solutions correct answers key 

1.      Suppose the following LPP together with its formulation and MS output: [b:4p., the rest 2p each

Innis Investments manages funds for a number of companies and wealthy clients. The investment strategy is tailored to each client’s 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 Innis’s 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 simply indicates that it is the riskier investment. Innis’s 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 (RI) for the portfolio.

Min RI=8S+3M  s.t. : ...S=stock funds; M= money market funds

a)      What is the optimal solution/complete conclusion?

b)      Considering the type of constraints, do values of 0; 0; 7000 represent slack or surplus?

I.                   0 ……

II.                0……

III.             7000……

What is the meaning/interpretation of 7000? You must be concrete in terms of the example.

…c-f questions will not be graded without explanations…

c)      Will the optimal solution change if the objective function is changed to RI=8S+9M? Explain.

d)     Will the optimal solution change if the objective function is changed to RI=6S+4M ? Explain.

e)      Will the optimal solution change if the first constraint is changed to 50S+100M1 000 000? Explain.

f)       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.

g)      What will happen to the optimal value of RI (62 000) if total budget is increased by $1?

h)      What is the interpretation of negative dual price of -2.167?

2.      Solve the LPP graphically: [12pts]

Max F= 3x+2y subject to:   

NOTE: Number each straight line with corresponding number of inequality. The final solution set

must be highlighted/cross-hatched. Identify/calculate all vertices of feasible set.

Conclusion: