Question

A person invests all of $100,000 in two stocks: Stock A has an expected annual return of 2% and a risk rating of 3 and stock B has an expected annual return of 7% and a risk rating of 9. The risk rating of the total investment is the weighted average of the risk ratings of the two investments. The person wants to maximize the total expected annual returns. However, to reduce risk, he requires that: (1) investment B be no more than 30% of the total and (2) the average risk rating of the total investment be no more than 5.

1a) Formula the person’s investment plan as a linear programming problem.

1b) Show graphically the feasible region of investment.

Answer 1

Let the amount invested in stock A be x and amount invested in stock B be y

Max Z = 0.02x + 0.07y (Profit maximization objective function)

subject to,

x+y<=100,000 (constraint-1 where maximum permissible investment cannot exceed $100,000)

(3x+9y)/x+y <=5 (constraint-2 where the average risk factor does not exceed 5)

x,y > 0 (non negativity constraint)

Max z = 30,000