### MATH 318: Spring 2008 Sample Final

The final exam for this class is open book/open note. You may use a calculator, ruler, pencil, pen and graph paper on the final. You may not use a cell phone calculator, computer, or any other device with the ability to communicate outside the classroom.  Record all answers and the work needed to justify them in the space you're given (you may continue an answer on the back of the page if you indicate where to look for it.)

How is this sample final related to the actual final exam? Before the last week of class I created a list of final exam questions. Half of those questions are on the sample final and half are on the final exam. Some questions on the final exam will be related to questions on the sample final (e.g. the same question appears on the final with some numbers changed or some information appears on both exams). The average question on the final exam is likely to be easier than the average question on the sample final. Do not expect the questions on the final exam to be of the same type or to cover exactly the same topics as the questions on the sample final.

1. (Problem 6, p. 87) The American Housing Survey reported the following data on the number of bedrooms in rented houses in central cities.  Compute the expected value and variance for number of bedrooms in rented houses.
2.  No. of Bedrooms 0 1 2 3 4 or more No. of Houses(thousands) 547 5012 6100 2644 557

3. The time (in minutes) between telephone calls at an insurance claims office has the exponential probability distribution f(x) = 0.50 e-0.50x for x > 0. What is the probability of 30 seconds or less between telephone calls?

4. Shown below is a crosstabulation of which Merry Melodies programmers received bonus pay, organized by gender.

a) Create a joint probability table for programmer bonuses.
b) If a programmer got bonus pay, what is the probability that that programmer was female?

 Bonus No Bonus Female 3 1 Male 7 2

5. Figure 4.17 on page 140 of your text shows a decision tree for the Dante Development Corporation.

a) What is the optimal decision strategy for Dante?
b) Develop a risk profile for this decision strategy.
c) If Dante wins the contract but does no market research, does the MiniMax Regret approach recommend building or selling?

6. Merry Melodies produces two software products: MusicMaker and Computer Cacaphony. They are trying to decide how many copies of each program to produce for the upcoming holiday season.
• Each box of MusicMaker software sold yields \$10 profit. Each Computer Cacaphony sold yields \$6 profit.
• Merry Melodies has enough space in a warehouse for 50 palettes of software. A palette holds 40 copies of MusicMaker software or 100 copies of Computer Cacaphony.
• Projected demand is for 1800 copies of Merry Melodies and 1500 copies of Computer Cacaphony.
• Merry Melodies' lawyers recommend that at least 40% of the software produced be Computer Cacaphony in order to avoid an antitrust suit.

a) Formulate a linear programming problem to decide how many of each to produce.
b) Solve that linear programming problem and give the amounts of each type of software Merry Melodies should produce.

7. (Problem 17, p. 548) The Porsche Shop is preparing an estimate for the repair of a 1964 model 356SC Porsche. The parts needed cost \$8000. Labor cost is \$400/day for the four tasks shown below:

 Activity Optimistic Most Probable Pessimistic A 3 4 8 B 5 8 11 C 2 4 6 D 4 5 12

Tasks B and C can both be started as soon as A completes, but task D cannot start until B and C are both completed.

a) Develop a project network.
b) What is the expected project completion time?
c) What is the probability that the job will take longer than the expected completion time?