A $38,000 coil winding and unwinding machine is estimated to provide additional value to production by $15 per unit. When the machine is operated at 58 units per hour, it needs to be cooled down after 4 hours of operation and receive minor maintenance for 15 minutes. When the machine is operated at 118 units per hour, it needs to be cooled down after 5 hours of operation and receive minor maintenance for 30 minutes. The production line runs 8 hours per day. If each maintenance check costs $625 and the machine has a useful life of 80,000 hours of operations, at what speed should the machine should be operated

Answer: 118 units per hour

Explanation:

At 58 units per hour:

The cycle time = 4 hours + 0.25 hours

= 4.25 hours

The cycle per day = 8/4.25 = 1.88 cycle

The value added per day will be:

= 1.88 * 4 * 58 * 15

= $6542.4

The cost of maintenance per day will be: = 1.88 * $625 = $1175

The cost of operating the machine per day will be:

= $38,000/80,000 * 4 * 1.88

= $3.57

The net increase in the value per day will be:

= $6542.4 - $1175 - $3.57

= $5363.83

At 118 units per hour:

The cycle time = 5 hours + 0.5 hours

= 5.5 hours

The cycle per day = 8/5.5 = 1.45 cycle

The value added per day will be:

= 1.45 * 5 * 118 * 15

= $12832.5

The cost of maintenance per day will be: = 1.45 * $625 = $906.25

The cost of operating the machine per day will be:

= $38,000/80,000 * 5 * 1.45

= $3.44

The net increase in the value per day will be:

= $128322.5 - $906.25 - $3.44

= $11922.81

The machine should be operated at 118 units per hour because it gives a higher value.