A manufacturer of high-quality small appliances intended for home use is currently working on the development of a new kitchen appliance that will chill foods quickly much as a microwave oven heats them quickly, although the technology involved is quite different. R&D engineers now have a working prototype and are satisfied that, with the cooperation from the production and marketing people, the product can be ready in time for the summer buying season. A target date has been set for product introduction that is 24 weeks away. One of the current issues for the company is that a competitor is also in the process of developing a similar product, which it intends to bring out at almost exactly the same time. The manager of the company is wondering whether it would be possible to expedite the usual product introduction process in order to beat the competition to the market. If possible, the manager would like to get a six week jump on the completion; this would put the product introduction date only 18 weeks away. Since the product of the company has been through the production-introduction process a number of times, the manager has developed a list of the tasks that must be accomplished and the order in which they must be completed. Although the duration and costs vary depending on the particular product, the basic process does not. The list of activities, the precedence relationships, activity durations, and costs estimates are presented in Table below. Note that some of the activities can be completed on crash basis, with an associated increase in cost. The company need to decide whether to bring the product to the market 18 weeks from now as the manager is recommending. For the project, indirect costs have been estimated at $5,500 per week. However, after week 18, if the product is not fully on the market, with each additional week the project investment value will reduce by $20,000. For every week the project is shortened to week 18 the manufacturer saves one week of investment value and indirect cost, or $25,500. For reduction beyond week 18, the savings are only the weekly indirect costs of $5,500. As the project manager specialist you have been asked to answer the following questions.

a. Develop an AON network diagram for the product and determine the number of paths and the critical path. How long does the project take using normal durations? What is the total cost required for completing the project on normal time?

b. Is it possible to complete the project in 18 weeks? What would the associated additional costs be? Which activities would need to be completed on a crash basis? What is the net savings from crashing the project to 18 weeks? What is the total cost required for completing the project in 18 weeks?

c. Is there some timeframe shorter than the 18 weeks recommended by the manager that would make sense in terms benefit-cost (i.e., what is the minimum-cost schedule?). What would be the total cost for completing in this timeframe?

d. What is the slack (in days) associated with noncritical paths through the project?