Question

1. 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 30% of the total and (2) the average risk rating of the total investment be no more than 5.

PLEASE SHOW ALL YOUR WORK! MAKE IT CLEAR! AND IF YOU SCAN YOUR PAPER MAKE IT DARKER

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

Answer 1

I think there is something missing in the question. In the second last line where there is 'The person wants to maximize 30% of the total', the statement should tell about maximise the returns and restricting the investment in any one stock to maximum of 30%.

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 = 0.02 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* 3 + y * 9 < 5 (limiting risk rating).