Question: Filter Systems produces air filters for domestic and foreign cars. One filter, part number JJ39877, is supplied on an exclusive contract basis to Oil Changers at a constant 200 units monthly. Filter Systems can produce this filter at a rate of 50 per hour. Setup time to change the settings on the equipment is 1.5 hours. Worker time (including overhead) is charged at the rate of $55 per hour, and plant idle time during setups is estimated to cost the firm $100 per hour in lost profit. Filter Systems has established a 22 percent annual interest charge for determining holding cost. Each filter costs the company $2.50 to produce; they are sold for $5.50 each to Oil Changers. Assume 6-hour days, 20 working days per month, and 12 months per year for your calculations.

a. How many JJ39877 filters should Filter Systems produce in each production run of this particular part to minimize annual holding and setup costs?

b. Assuming that it produces the optimal number of filters in each run, what is the maximum level of on-hand inventory of these filters that the firm has at any point in time?

c. What percentage of the working time does the company produce these particular filters, assuming that the policy in part (a) is used?