21. The time study data of an equipment deployed in a mine during a calendar month is given below.
Total working hours = 400
Total maintenance hours = 100
Total hours of actual work = 240
The percentage of utilization of the equipment is
Total working hours = 400
Total maintenance hours = 100
Total hours of actual work = 240
The percentage of utilization of the equipment is
22. In an opencast mine loading and transporting has been carried out by shovel dumper combination. There is only one shovel is in operation. Dumpers arrive at the rate of 10 dumpers per hour and it takes shovel on an average 5 minutes to load a dumper. Assume arrival is Poisson and service time is exponentially distributed. Find the expected number of dumpers in the system.
23. ISO 9000 Quality Systems DO NOT contain
24. The following project network is given with arrows as activities and the numbers by each arrow representing job durations in days. The network has two dummy activities D1 and D2. The minimum completion time of the project in days is
25. A balanced transportation problem is characterised by
26. The feasible region of an LP problem is shown as given below. The maximum value of the objective function Z = 1600X1 + 1200X2 is
27. In an opencast mine loading and transporting has been carried out by shovel dumper combination. There is only one shovel is in operation. Dumpers arrive at the rate of 10 dumpers per hour and it takes shovel on an average 5 minutes to load a dumper. Assume arrival is Poisson and service time is exponentially distributed. Find the probability that the shovel is sitting idle.
28. There are 50 lemon trees in a reclaimed mine area. Each tree produces 800 lemons per year. For each additional tree planted in this area, considering all trees, the output number of fruits per tree drops by 10 lemons in a year. The number of trees that to be added to the existing reclaimed area in order to maximise the total number of lemons in the year is
29. In an opencast mine loading and transporting has been carried out by shovel dumper combination. There is only one shovel is in operation. Dumpers arrive at the rate of 10 dumpers per hour and it takes shovel on an average 5 minutes to load a dumper. Assume arrival is Poisson and service time is exponentially distributed. What is expected waiting time of the dumper in the queue?
30. A mining project is composed of five activities whose three time estimates
in months are given below:
Activity
Estimated duration (months)
Optimistic time
Most likely time
Permissible time
1-2
1
1
7
1-3
2
5
8
2-4
1
1
7
3-4
2
5
14
4-5
3
6
15
The standard deviation of the project length in months is
| Activity | Estimated duration (months) | ||
| Optimistic time | Most likely time | Permissible time | |
| 1-2 | 1 | 1 | 7 |
| 1-3 | 2 | 5 | 8 |
| 2-4 | 1 | 1 | 7 |
| 3-4 | 2 | 5 | 14 |
| 4-5 | 3 | 6 | 15 |