Midterm Exam 1 (October 20, 2021)

Discussion version, posted for all sections

Question 1 (40 points)

The manager of the fresh fruit  section  at Jersey Foods wants to order raspberries today for tomorrow’s needs. Since these raspberries are ripe, Jersey Foods will need to sell them tomorrow and then discard the items that remain unsold. (Note that this is a simplification of reality.) The manager estimates that Jersey Foods will sell  12, 13, 14, or 15 cases tomorrow. Cases consist of 6 smaller packages: for simplicity, we consider only entire cases as the unit to consider. Jersey Foods purchases the raspberries for $7 per case and sells them for $18 per case. The manager checked their recent records on daily raspberry sales: based on this information, she estimates the probabilities for selling 12, 13, 14, and 15 cases of raspberries tomorrow are 0.1, 0.3, 0.4, and 0.2, respectively.

1.1  Develop  a  decision  analysis  formulation  of  this  problem,  by  identifying  the  decision alternatives, the states of nature, and display the payoff table.

1.2 How many  cases  of raspberries  should  be  purchased,  according  to  the  maximin  payoff criterion?

1.3 How many cases should be purchased according to the maximum likelihood criterion?

1.4 How many cases should be purchased according to Bayes’ decision rule?

1.5 The manager is a bit uncertain about the probability estimates for selling  13 cases and 14 cases. Reapply Bayes’ decision rule when the prior probabilities of selling 13 and 14 cases are (i) 0.2 and 0.5, (ii) 0.4 and 0.3, and (iii) 0.5 and 0.2.

1.6 What seems to be the most reasonable final decision, regarding the order volume?

Question 2 (20 points)

You developed a new software product to play high-quality video games on a computer. The software has unique features that you patented. However, it appears that some of these features were  copied  and  used  in  a  competitive  software  product  recently  released  by  MegaVideo Corporation. Therefore, you consider suing MegaVideo for patent infringement. With legal fees and other expenses, your cost of going to trial is expected to be $1 million. You think that you have a 60% chance of winning the case, in which case you would receive $5 million in punitive damages. If you lose the case, then you will receive nothing. Moreover, in the latter case, there is a 50% chance that the judge would also order you to pay for court expenses and legal fees incurred by MegaVideo implying an additional cost of $1 million. As an alternative to consider, MegaVideo has offered you $1.5 million to settle this case out of court.