Ralph Smart, the owner of the Blackburn Garage, is considering the possibility of becoming a Silencer Muffler franchisee. The garages current operations consist of four service bays (areas). These areas are: (a) tune-ups, (b) lubrication and oil change, (c) wheel alignment, and (d) transmission repair. Each service bay is dedicated to a specific type of auto repair, so only one type of repair can be made in each bay. For internal control purposes, Ralph uses a job-order, standard, full-absorption, usage-based costing system to accumulate costs for each job/repair. Parts are charged at their procurement cost. Labor and overhead (OH) costs are combined into one cost pool and jointly charged to each job at a rate of $36 per mechanic hour. This rate is comprised of: (a) a variable labor cost of $15 per hour, (b) variable overhead rate of $5 per labor hour and (c) a fixed overhead rate of $16 per labor hour.

Ralph estimates the following profits for a typical job in each of the four service areas:

Tune-Up Lube & Oil Wheel Alignment Trans. Repair

Price $59 $20 $30 $380

Parts Cost 12 8 3 200

Allocated Costs 36 9 21 144

Profit per job $11 $ 3 $ 6 $ 36

Blackburn currently employs four mechanics, each of whom may work a maximum of 36 hours per week and 48 weeks per year. Mechanics are only paid for hours actually spent repairing cars. Because of space limitations, no more than four mechanics may be employed. Operating additional shifts (i.e., expanding the total amount of available labor) is not an option.

Ralph would buy the Silencer mufflers for $25 each and it is expected that, on average, installation time would be 30 minutes. The variable overhead rate for this work will be the same as for other repairs. Total fixed costs are expected to remain the same.

Because of facility requirements, mufflers can only be installed in the following bays: Tune-Up, Lube & Oil, and Transmission Repair. In each of these bays, muffler work may be interchanged with the normal work of that bay and there are no delays in switching between muffler work and the normal work of that bay. Only one mechanic may work in one service bay at a time, so even if there is a mechanic at another bay who is not working, he/she cannot help out a mechanic in another bay.

The expected annual demands (expressed in terms of repair hours) at the current prices in Tune-Up (TU), Lubrication and Oil (LO), Wheel Alignment (WA) and Transmission Repair (TR), are 1,600, 1,500, 1,825, and 1,950 hours, respectively.

The demand for each service is independent of the demand for other services. The Silencer Company requires that any franchisee must give the muffler customer priority service and that prices must be the same to all muffler customers. Any franchisee failing to do this is terminated. The practical consequence of this requirement is that the demand for mufflers must be met first before non-muffler customers if Blackburn becomes a franchisee, regardless of how profitable muffler repairs are compared to the other types of repairs.

A. Assume that Ralph becomes a Silencer Muffler franchisee. How many mufflers should be installed in each bay during the year in order to maximize profits if the expected annual demand for mufflers is 1,000 units? Hint: You dont need to know how much Ralph will charge for the muffler. (i) Tune-Ups: (ii) Lube & Oil: (iii) Wheel Alignment: (iv) Trans. Repair:

B. Assume that Ralph becomes a Silencer Muffler franchisee. How many mufflers should be installed in each bay during the year in order to maximize profits if the expected annual demand for mufflers is 8,200 units? (i) Tune-Ups: (ii) Lube & Oil: (iii) Wheel Alignment: (iv) Trans. Repair:

C. At an annual demand of 8,200 muffler units, what is the price for muffler installations that Ralph should charge such that he expects to make the same level of profits if he becomes a muffler franchisee as he would expect to make without becoming a muffler franchisee?