Sheila earned an $80,000 bonus which she would like to invest in the stock market. She is planning to buy shares of AMI Inc. and BCM Corp. The expected annual return for AMI is $3 per share and the annual return for BCM is $5 per share. AMI costs $25 per share and BCM costs $50 per share. Sheila would like to limit the risk in her stock portfolio. The risk is 0.50 per share of AMI and 0.25 per share of BCM. She wants the total risk of her stock portfolio to be at most 700. In addition, to make sure the portfolio is diversified she wants to invest in no more than 1,000 shares of AMI.
(a) Formulate a linear optimization model that Sheila could use to decide how many shares of each stock to buy in order to maximize the total expected annual return of the portfolio subject to the constraints.
(b) Use Excel to solve the linear optimization problem.
(c) How many shares of each stock should Sheila purchase?
(d) What is the expected annual return of the portfolio?
(e) Which constraints are binding?