Problem 1: A car dealer is trying to determine how many 2008 cars to order in the end of the second quarter of 2007. Each car ordered in the end of the second quarter of 2007 costs $10,000. The demand for the dealer's 2008 model has the probability distribution shown below. Each 2008 car sells for $15,000.

If demand for 2008 cars exceeds the number of cars ordered in the end of 2007 , the dealer must reorder at a cost of $12,000 per car. At the end of year 2008 excess cars can be sold to the rental car market at $9,000 per car.

1. Use simulation with 1000 replications to determine the optimal number of cars to order in the end of the second quarter of 2007.
2. Find a \(95 \%\) confidence interval of the optimal expected profit with 1000 replications.
3. Use 50 preliminary replications to find the number of replications such that the optimal expected profit has a max margin of error $2,000.

Problem 2: A company's new product development track record shows that the probability of getting

a patent for its new product is 0.43, and the probability of a new product being profitable is 0.55. The conditional probability of being profitable given that the new product didn't get a patent is 0.35. What is the conditional probability of being profitable given that the new product does get a patent (give your answer to 4 decimal places)?

Problem 3: Lands' End Direct Merchants is trying to decide whether to ship some customer orders now via UPS or wait until after the threat of UPS strike is over. If Lands' End decides to ship the requested merchandise now and the UPS strike takes place, the company will incur $60,000 in delay and shipping costs. If Lands' End decides to ship the customer orders via UPS and no strike occurs, the company will incur $4,000 in shipping costs. If lands' End decides to postpone shipping its customer orders via UPS, the company will incur $10,000 in delay costs regardless of whether or not UPS goes on strike. Let \(p\) represent the probability that UPS will go on strike and affect Lands' End's shipments.

1. For which values of \(p\), does Lands' End minimize its expected total cost by choosing to postpone shipping its customer orders via UPS (give your answer to 4 decimal places)?
2. Suppose Lands' End can purchase information regarding the likelihood of the UPS strike in the near future. Compute the expected value of perfect information (EVPI) when \(p=0.15\).

Price: $13.46

Solution: The downloadable solution consists of 6 pages, 746 words and 2 charts.
Deliverable: Word Document