Module A Problems
Problems A.8, A.21, A.22, A.23, and A.24
The specifications for these homework problems and the grading rubric can found in the Homework Problems section under Introduction & Resources.
Submit your assignment by the due date.
A.8 Leah Johnson, director of Urgent Care of Brookline, wants to increase capacity to provide low-cost flu shots but must decide whether to do so by hiring another full-time nurse or by using part-time nurses. The table below shows the expected costs of the two options for three possible demand levels:
| STATES OF NATURE | |||
| Alternatives | Low Demand | Medium Demand | High Demand |
| Hire full-time | $300 | $500 | $700 |
| Hire part-time | $0 | $350 | $1,000 |
| Probabilities | .2 | .5 | .3 |
- Using expected value, what should Ms. Johnson do?
- Draw an appropriate decision tree showing payoffs and probabilities.
A.21 Ronald Lau, chief engineer at South Dakota Electronics, has to decide whether to build a new state-of-the-art processing facility. If the new facility works, the company could realize a profit of $200,000. If it fails, South Dakota Electronics could lose $180,000. At this time, Lau estimates a 60% chance that the new process will fail.The other option is to build a pilot plant and then decide whether to build a complete facility. The pilot plant would cost $10,000 to build. Lau estimates a 50–50 chance that the pilot plant will work. If the pilot plant works, there is a 90% probability that the complete plant, if it is built, will also work. If the pilot plant does not work, there is only a 20% chance that the complete project (if it is constructed) will work. Lau faces a dilemma. Should he build the plant? Should he build the pilot project and then make a decision? Help Lau by analyzing this problem.
A.22 Dwayne Whitten, president of Whitten Industries, is considering whether to build a manufacturing plant in north Texas. His decision is summarized in the following table:
| Alternatives | Favorable Market | Unfavorable Market |
| Build large plant | $400,000 | –$300,000 |
| Build small plant | $80,000 | –$10,000 |
| Don’t build | $ 0 | $ 0 |
| Market probabilities | 0.4 | 0.6 |
- Construct a decision tree.
- Determine the best strategy using expected monetary value (EMV).
- What is the expected value of perfect information (EVPI)?
A.23 Deborah Kellogg buys Breathalyzer test sets for the Winter Park Police Department. The quality of the test sets from her two suppliers is indicated in the following table:
| Percent Defective | Probability For Winter Park Technology | Probability For Dayton Enterprises |
| 1 | .70 | .30 |
| 3 | .20 | .30 |
| 5 | .10 | .40 |
- For example, the probability of getting a batch of tests that are 1% defective from Winter Park Technology is .70. Because Kellogg orders 10,000 tests per order, this would mean that there is a .70 probability of getting 100 defective tests out of the 10,000 tests if Winter Park Technology is used to fill the order. A defective Breathalyzer test set can be repaired for $0.50. Although the quality of the test sets of the second supplier, Dayton Enterprises, is lower, it will sell an order of 10,000 test sets for $37 less than Winter Park
- Jabiru/Shutterstock
- Develop a decision tree.
- Which supplier should Kellogg use?
A.24 Joseph Biggs owns his own ice cream truck and lives 30 miles from a Florida beach resort. The sale of his products is highly dependent on his location and on the weather. At the resort, his profit will be $120 per day in fair weather, $10 per day in bad weather. At home, his profit will be $70 in fair weather and $55 in bad weather. Assume that on any particular day, the weather service suggests a 40% chance of foul weather.
- Construct Joseph’s decision tree.
- What decision is recommended by the expected value criterion?