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