Rutgers University, School of Business — New Brunswick



Professor Jonathan Eckstein

Operations Management, 33:623:386:01/02

School of Business – New Brunswick

Rutgers University

Review Material for First Midterm Exam

Spring 2002

You will have 80 minutes. You will write all answers in the “blue books” provided. The exam will have two questions. One will be spreadsheet question and the other an algebra question. They will be on different topics.

Allowed materials:

• A single “cram sheet” in your own handwriting (both sides allowed)

• A dictionary (if English is not your first language)

• A calculator

The best way to prepare for the exam is to work example problems such as the ones in this handout. Memorizing material from the book is not likely to be very helpful. Making up a cram sheet can be helpful, but I rarely see students referring to their cram sheets during the exam.

Note that while I use a TA or grader to grade homework assignments, I generally grade all exams myself. I can be quite persnickety about the following items. They do not usually count for a lot of points, but you should be aware of them:

• In algebra models, define all your decision variables precisely as measurable numbers like “the number of gallons of yogurt produced,” not just “yogurt”.

• In the spreadsheet problems, try to refer to the given data of the model using cell references. For example, if the unit cost of labor is $25/hour, shown in the spreadsheet as a 25 in cell C3, and the hours of labor used is in E20, then C3*E20 would be a better formula for labor cost than 25*E20. The reason is that if the cost of labor changes, somebody using the spreadsheet can just change the obvious data in C3 and not have to examine every formula in the spreadsheet.

• Sometimes I will ask that you write formulas that will yield correct results when copied to other cells. That means you have to correctly decide whether to put $ absolute references into your formulas, and where.

• Use correct syntax when writing Excel formulas (if you tend to forget the syntax, that might be a good thing for your cram sheet).

The following pages give sample problems from past exams. A few have been altered because of slight changes in the material covered.

1: Designing a Portfolio

You have been asked to design a portfolio of stocks and bonds issued by six different companies. The relevant information is in the following table.

| |Stocks |Bonds |

|Company | | |

| |Expected Rate |Risk |Expected Rate |Risk |

| |of Return |Rating |of Return |Rating |

|AeroGiant |12.000% |5 |8.500% |2 |

|MacGulp |13.000% |4 |8.000% |1 |

|Netsco |20.000% |6 |9.500% |3 |

|Speculon |25.000% |10 |11.000% |6 |

|Allied Conglomerate |10.000% |4 |8.250% |2 |

|Zeroid |17.000% |7 |9.250% |3 |

For convenience, both stock and bond investments are denominated in dollars. The expected rates of return are for the coming year. Your client wants to invest exactly $100,000, and is willing to tolerate an average risk rating of at most 5. Assume that the portfolio’s average risk rating can be computed by averaging the risk ratings of the securities in the portfolio, weighting each security by its fraction of the total dollars invested. The portfolio must also conform to the following additional constraints, which are also intended to limit overall risk:

• At most 70% of the total portfolio may be invested in stocks.

• At most 65% of the total portfolio may be invested in bonds.

• Of the amount invested in stocks, no more than 35% may be invested in the stock of any single company.

• Of the amount invested in bonds, no more than 40% may be invested in the bonds of any single company.

• No more than 30% of the total portfolio may be invested in the combined stocks and bonds of any single company.

Subject to all these constraints, you would like to construct a portfolio with the greatest possible expected return for the coming year. To this end, you are using the spreadsheet model on the next page, which contains an optimal solution. Cells shaded like [pic] contain formulas. The average risk limit is enforced by the Solver constraint B30 = 0, B16:B22 = 0, and C16:C22  ................
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