2. An underground mine uses four mine trucks in its production plan. The running
ID: 3361250 • Letter: 2
Question
2. An underground mine uses four mine trucks in its production plan. The running time for the trucks has a normal distribution with a mean () of 22 hours and a standard deviation () of 5 hours. The running time for each truck is defined by the following equation: Running time + × (normal random number) From past performance, the time required to repair a truck is given by the following frequency distribution: Repair Time: Frequency: Ihr 2hrs 3hrs 4hrs 15 35 30 20 The cost of waiting while a truck is down is $135/hr. The cost for cach mechanic (who must be paid even if not working) is $11/hr. The priority of repair is 1st down-1t repaired. 1) Prepare a probability density distribution histogram for the repair time. 2) Plot the cumulative probability distribution function for the repair time 3) Using a GANNT chart approach, perform a manual simulation of 100 hours of operation for trials of one (1) and two (2) mechanics. Use the fourth column of uniform and normal random numbers for this simulation, as needed. 4) Tabulate the results of the two trials showing total running time, total repair time, and total waiting on repair time. What number of mechanics (1 or2) would you hire to minimize costs? How much money would you save with your selection in *5) above, over a period of one year? 5) 6) (Assume one year 16hrs/day 365days/year-5840hours/year).Explanation / Answer
Repair time frequency Interval frequency distribution (Probaility) probable range 1 15 0-1 15/100=0.15 0-14 2 35 1-2 35/100=0.35 15-49 3 30 2-3 30/100=0.3 50-79 4 20 3-4 20/100= 0.2 80-99
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