Question

in a factory, the machine breakdown occur on an average rate of 10 machines per hour. the idle time cost of a machine is estimated to be rs. 20 per hour. the factory works 8 hours a day. the factory manager is considering 2 mechanics for repairing the machines. the first mechanic a takes about 5 minutes on an average to repair a machine and demands wages rs. 10 per hour. the second mechanic b takes about 4 minutes in repairing a machine and demands wages at the rate of rs. 15 per hour. assuming that the rate of machine breakdown is poisson-distributed and the repair rate is exponentially distributed, which of the two mechanics should be engaged?

Answer 1

After calculating the total costs for both mechanics, considering their wages and machine idle time, Mechanic A is the more cost-efficient option with a total cost of Rs. 80 compared to Rs. 120 for Mechanic B.

Step-by-step explanation:

To decide whether to engage Mechanic A or B, we need to calculate the total expected cost for each mechanic, considering both wage and machine idle time costs. Finally, we will compare these costs to make an informed decision.

Calculations for Mechanic A:

• Average repair time: 5 minutes per machine
• Hourly wage: Rs. 10
• Machines repaired per hour: 60 / 5 = 12 machines
• Total wage cost for 8 hours: 8 * Rs. 10 = Rs. 80
• Since Mechanic A can repair more machines than the average breakdown rate, no idle machine costs are incurred.
• Total cost for Mechanic A: Rs. 80 (wage cost) + Rs. 0 (idle machine cost) = Rs. 80

Calculations for Mechanic B:

• Average repair time: 4 minutes per machine
• Hourly wage: Rs. 15
• Machines repaired per hour: 60 / 4 = 15 machines
• Total wage cost for 8 hours: 8 * Rs. 15 = Rs. 120
• Like Mechanic A, Mechanic B can repair more machines than the average breakdown rate, so no idle machine costs are incurred.
• Total cost for Mechanic B: Rs. 120 (wage cost) + Rs. 0 (idle machine cost) = Rs. 120

Comparing the total costs for both mechanics, Mechanic A has a lower total cost of Rs. 80 compared to Rs. 120 for Mechanic B. Therefore, the factory should engage Mechanic A to minimize costs.