Question

A milling machine is used to process an automobile part. The processing time per part is 4 minutes. After producing 190 units of the part, the milling machine requires a 34 minute maintenance process. Demand for the part is 12 units per hour.

What is the maximum inventory of a part (in units)?

Answer 1

The maximum inventory of the part is 158.8 units.

Step-by-step explanation:

The maximum inventory of a part can be calculated by determining the production rate and the demand rate. In this case, the processing time per part is 4 minutes and the demand for the part is 12 units per hour. To calculate the maximum inventory, we need to find the time it takes to produce 190 units, subtract the maintenance time, and divide by the demand rate:

Production time = 190 units * 4 minutes per unit = 760 minutes

Total time = Production time + Maintenance time = 760 minutes + 34 minutes = 794 minutes

Maximum inventory = Total time / (60 minutes per hour) * Demand rate = 794 minutes / (60 minutes per hour) * 12 units per hour = 158.8 units.

Therefore, the maximum inventory of the part is 158.8 units.

Answer 2

The maximum inventory of the part is approximately 280.8 units approximately, 280units

Calculating the time for one cycle (processing + maintenance):

Total time per cycle = Processing time + Maintenance time = 4 minutes/part + 34 minutes = 38 minutes/cycle

Calculating the number of cycles per hour:

Cycles per hour = 60 minutes/hour / Cycle time = 60 minutes/hour / 38 minutes/cycle = 1.58 cycles/hour (round to two decimal places)

Calculating the production rate per cycle:

Parts produced per cycle = Demand per hour / Cycles per hour = 12 parts/hour / 1.58 cycles/hour = 7.6 parts/cycle (round to two decimal places)

Determining the maximum inventory:

Maximum inventory = (Production per cycle - Demand per hour) * Cycle time

Maximum inventory = (7.6 parts/cycle - 12 parts/hour) * 38 minutes/cycle

Maximum inventory = (7.6 parts/cycle - 0.2 parts/cycle) * 38 minutes/cycle

Maximum inventory = 7.4 parts/cycle * 38 minutes/cycle = 280.8 minutes (round to one decimal place)

Therefore, the maximum inventory of the part is approximately 280.8 units approximately, 280units