Question

You are the manager of a manufacturing plant that produces disk drives for personal computers. One of your machines produces a part that is used in the final assembly. The width of this part is important to the disk drive’s operation. The width needs to be 4mm 005mm. If not, the disk drive will not work properly and will need to be repaired at a cost of $10.45.

The machine producing the part can be set to produce the part 4mm in width, but is not perfectly accurate. The actual width of the part produced is normally distributed with mean of 4mm and a variance that depends on the speed of the machine. If the machine is run at a slow speed, the width of the parts has a standard deviation of 0.002mm. At medium speed, the standard deviation of parts produced is 0.0025mm. At a higher speed, the machine is even less precise and produces parts with a standard deviation of 0.003mm.

At higher speed, more parts can be made per hour, reducing the per unit cost to $20.15, before repair costs. At medium speed, the per unit cost is $20.55 before repair costs. At the slower speed, the per unit cost before repairs is $20.95. As manufacturing manager, you want to produce the parts at the lowest average cost including repair costs. At what cost would the optimum speed produce parts?

Answer 1

When the width is out side , the disk drive requires repair.

If the machine is run at a slow speed, the probability of repair is

If the machine is run at a medium speed, the probability of repair is

If the machine is run at a high speed, the probability of repair is

Average unit cost at Low speed is

Average unit cost at medium speed is

Average unit cost at high speed is

The average unit cost is minium for medium speed. So the optimum speed is medium speed.

The unit cost at this speed is .