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QUESTION A

You are in charge of a medium-size real estate development project in Los Angeles County. You have attracted $100 million in capital to fund this project, over which you are paying 6% interest per year.

The first step you need to do is the architectural design, which will take 6 months. After that, you will do additional market research, to ensure the demand is still there; that will take 4 months. After the market research, you can start marketing the project to prospective buyers. In parallel to the market research, you need to complete an environmental impact assessment (EIA), which can take anywhere between 2 months and several years. After the additional market research and the EIA are completed, you can start construction.

Construction starts with the underground work: water mains, sewage, etc., which takes 3 months. After that, building homes takes 6 months, and building roads also takes 6 months; homes and roads can be built simultaneously.

Marketing involves first designing an advertising campaign, which takes 2 months; then the actual advertising itself, which takes 4 months; then the sales period, which takes 4 months.

After construction and marketing are complete, the new owners can move in to their brand new home.

a) Draw a visual representation of this project. (Activity-on-Nodes diagram, Gantt chart, whichever format you prefer.)

b) Assume the EIA only takes 2 months to be approved. What is the critical path of this project? How long will it take before the new owners move in?

c) What does the critical path tell you?

d) You are very unlucky, and the only rain storm of the year occurs while you are in the midst of construction, leading to a delay. How much delay (if any) can you accept before getting worried?

QUESTION B

A specialty coffee house sells Jamaican Blue Mountain Coffee at a fairly steady rate of 280 pounds annually. The beans are purchased from a local supplier for $2.40 per pound. The coffee house estimates that it costs $45 in paperwork and labor to place an order for the coffee and that holding costs are based on a 20% annual interest rate.

a) Determine the optimal order quantity for Jamaican Blue Mountain Coffee.

b) What is the time between placement of orders?

c) What is the average annual cost of holding and setup due to this item?

d) If the replenishment lead-time is three weeks, determine the reorder point based on the on-hand inventory.

QUESTION C

Consider a single-stage, single-server system with a Poisson arrival rate of 50 customers per hour, and an exponential service rate of 75 customers per hour.

a) Compute system utilization, average time in system and average number in system.

b) Compute The Same system Characteristics (utilization,average time in system and average number in system) for: i) an arrival rate of 20 customers per hour and ii) an arrival rate of 70 customers per hour assuming an exponential service rate of 75 customers per hour for both cases.

c) From part (b), what is a good value for utilization of the system? (Hint: This is a qualitative question.)

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Question D

Jane and Joe are the catering committee members for the C4C Casino Night and need to decide how many pretzels to order. The pretzels cost $0.10 and sell for $0.25; unsold pretzels can be returned to the supplier for a $0.05 refund (the supplier then sells them in its Day Old Shopper for $0.15). Demand is estimated to be normal with a mean of 500 and standard deviation of 100.

a) How many pretzels should they order?

b) Suppose demand has standard deviation of 200. How many pretzels should be ordered now? What can you say about the relationship between order quantity and demand uncertainty (standard deviation)?

c) Due to a surge in pretzel demand, the cost per pretzel to Jane and Joe goes up to $0.18; however, due to the extreme price-elasticity of Anderson students, they can still only sell them for $0.25. Unsold pretzels still only fetch $0.05 upon return. Determine how many pretzels Jane and Joe should order, assuming standard deviation of demand is 100 and 200. What do you note?

d) Suppose Jane and Joe decide to set the probability of a stock out at 10% (i.e., the probability that total demand exceeds the order quantity is 10%). How many pretzels should be ordered if standard deviation of demand is 200?

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