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1. (Chapter 7 in Edition 4 – Question 36)Add a new stock, stock 4, to the model in Example 7.9. Assume that the estimated mean andstandard deviation of return for stock 4 are 0.125 and 0.175, respectively. Also, assume thecorrelations between stock 4 and the original 3 stocks are 0.3, 0.5, and 0.8. Run Solver onthe modified model, where the required expected portfolio return is again 0.12. Is stock in theoptimal portfolio? Then run SolverTable as in the example. Is stock 4 in any of the optimalportfolios on the efficient frontier?

2. (Chapter 7 in Edition 4 – Question 54)A company manufactures two products. If it charges price pi for product i, it can sell qi unitsof product i, where q1 = 60 − 3p1 + p2 and q2 = 80 − 2p2 + p1. It costs $5 to produce a unit ofproduct 1 and $12 to produce a unit of product 2. How many units of each product should thecompany produce, and what prices should it charge, to maximize its profit?

3. (Chapter 8 in Edition 4 – Question 15: Classification)Review Section 8.8 on Clustering Analysis.The file P08-15.xlsx contains the following information about the top 25 MBA programs (accordingto the 1997 Business Week Guide): percentage of applicants accepted, percentage ofaccepted applicants who enroll, mean GMAT score of enrollees, mean undergraduate GPA ofenrollees, annual cost of school (for state schools, this is the cost for out-of-state students),1percentage of students who are minorities, percentage of students who are non-U.S. residents,and mean starting salary of graduates (in thousands of dollars). Use these data to divide thetop 25 schools into 4 clusters using the clustering approach in Section 8.8. Then interpret yourclusters.