Question

A person plans to invest up to $10,000 in two stocks: stock A with an expected annual return of 1% and a risk rating of 2 and stock B with an expected annual return of 7% and a risk rating of 8. The risk rating of a combinated investment is the weighted average of the risk rating of the individual investments. The person wants to (1)maximize 60% of the total and (2) the average risk rating of the combined investment cannot exceed 5. 1a. Formulate the person's investment plan as a linear programming problem. 1b. Show graphically the feasible region of investment and develop a typical iso-return line.

Answer 1

FORMULATION OF LINEAR PROGRAMMING ARE AS FOLLOWS:

Let the amount to invest in Stock A is 'x' and in Stock B is 'y'.
Objective function (Maximisation) = Z = 0.01 x + 0.07 y

Constraint functions:
x + y < $100,000
x < 0.30 * $100,000 i.e. x < $30,000 (If investment amount to restrict is in Stock A).
y < 0.30 * $100,000 i.e y < $30,000 (If investment amount to restrict is in Stock B).
x* 2 + y * 8 < 5 (limiting risk rating).

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