Suppose Clutch-o-Matic, Inc., has been approached by an automotive company to pr

Question

Suppose Clutch-o-Matic, Inc., has been approached by an automotive company to provide a particular model of clutch on a daily basis. The automotive company needs 1400 clutches per day, but expects to divide this production among several. Supplier’s. What the company wants from Clutch-o-Matic is a commitment to supply a specific number each day (i.e., a daily quota). Under the terms of the contract, failure to supply the quota will result in a financial penalty. Clutch-o-Matic has a line it could dedicate to this customer and has computed that the line has a mean daily production of 400 clutches with a standard deviation of 50 clutches under single (eight-hour) shift production.

A clutch sells for $280, of which $30 is profit. If overtime is used, union rules require at least two hours of overtime pay. The cost of worker pay, supervisor pay, utilities, etc., for running a typical overtime shift has been estimated at $5,500.

a. What is the profit-maximizing quota from the perspective of Clutch-o-Matic?

b. What is the average daily profit to Clutch-o-Matic if the quota is set at the level computed in a?

c. If the automotive company insists on 250 clutches per day, is it still profitable for Clutch-o-Matic? How much of a decrease in profit does this cause relative to the quota from b? How might a quota-setting model like this one be used in the negotiation process between a supplier and its customers requesting JIT contracts?

Explanation / Answer

Range of Production per day = Mean - SD to Mean + SD = 400+-50 = 350 to 450

Since we don’t have the data regarding the financial penalty let’s consider the profit maximizing number without the Overtime is 400

Hence Total profit = 400*30 = $ 12000

In 2 hours of overtime, Number of Clutches that can be produced is 400/ (8/2) = 100

Selling price of the 100 Clutches produce in overtime = 100*280 = 28000

Cost incurred = 5500

Profit over the 100 Clutches = 28000- 5500 = 22500

Profit per item = 22500/100 = 225

Decrease in profit = 34,500 - 7,500 = $ 27,000

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