Norcen Industries, a job shop specializing in close-tolerance manufacturing, has just accepted a $100,000 contract to provide machined parts to the Department of Defense. Production cost (direct labor, materials and overhead) is estimated to be $60,000. The due date for the delivered parts is June 30th. Given the uncertainties of manufacturing this order (and the uncertainties of job shop management in general), Norcen is considering what the planned leadtime for this job should be; i.e., how many months in advance of June 30th the job should be released to the shop. Once the job is released to the shop, the following leadtimes (and associated probabilities) are possible:

Actual Leadtime Probability 4 Months 0.1 5 " 0.2 6 " 0.3 8 " 0.2 9 " 0.2 f the job is completed in advance of its due date, Norcen must hold it in inventory at an estimated cost of $2,000 per month. If, on the other hand, Norcen fails to meet the due date, Norcen must pay a "tardiness" penalty of $5,000 per month. a. If 5 months is the chosen planned leadtime, what is Norcen's expected inventory holding cost? b. If 6 months is the chosen planned leadtime, what is Norcen's expected penalty cost? c. How many months in advance of June 30th should Norcen release the order to the shop? What is the Total Expected Profit associated with this optimal planned leadtime?