A company has to decide at what speed it should run its production machines. The

Question

A company has to decide at what speed it should run its production machines. The below table provides the results after analyzing the operational effectiveness of a production machine at two different speeds: A set of unsharpened tools costs $1,500 and can be ground 15 times. The cost of each grinding is $20. The time required to change and reset the tools is 2 hours, and such changes are made by a tool-setter who is paid $16/hour. The production machine operator is paid $15/hour, including the time that the machine is down for tool sharpening. Variable overhead on the machine is charged at the rate of $30/hour, including tool-changing time. At what speed should the machine be operated to minimize the total cost per piece?

Explanation / Answer

Calculate the total cost for both the speeds individually as follows for particular set of tools. For Speed A Output = 450*10*15 = 67500 pieces (multiplying 15 because for a toolset the total production output is calculated) Total cost = Tool cost + Grinding cost + Tool setter cost + Operator cost + variable overhead cost = 1500 + 20*67500 + 15*2*16 + (10+2)*15*15 + (10+2)*15*30 = 1500 + 1350000 + 480 + 8100 = 1360080 Total cost per piece = 1360080/ 67500 = 20.149 For speed B Output =500*8*15 = 60000 pieces (multiplying 15 because for a toolset the total production output is calculated) Total cost = Tool cost + Grinding cost + Tool setter cost + Operator cost + variable overhead cost = 1500 + 20*60000 + 15*2*16 + (8+2)*15*15 + (8+2)*15*30 = 1500 + 1200000 + 480 + 6750 = 1208730 Total cost per piece = 1208730/ 60000 = 20.145 So Answer should be Speed B should be chosen.

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