You have been granted with a chance of profit. Someone from your family lent you $100,000 without any interest rate, for one year. You have two options to invest this capital, so that when you pay your debt back next year, the earnings from the investments would be your profit. You can either invest in a government bond, or a risky stock. Return and risk score of the bond and the stock are shown in the table.

BOND = 3% RISK SCORE = 2 STOCK= 8% RISK SCORE = 5

The average risk score of your portfolio cannot exceed 3.2. On the other hand, the same relative asked you to decide your portfolio such that the amount you invested in the bond cannot exceed the amount you invested in stock by more than $40,000.

a.) Formulate an LP model that solves for the portfolio with maximum return without exceeding an average risk score of 3.2 and the amount you invest in bonds can be at most $40,000 more than the amount you invest in stock.

b.) Solve your model using graphical method.

c.) What would be the sign of the shadow prices (i.e. positive, negative or zero) of the constraints in your model? (You don’t need to answer that for total investment constraint as obviously with higher budget you would get more return) (2 points)