1. Workmen arrive at a mine workshop to receive tools for maintenance. The inter-arrival time of workmen at the service counter is exponentially distributed with an average time of 10 min. The service time at the counter is also distributed exponentially with a mean time of 6 min. The average time spent by a workman waiting for his turn to be served in min is
2. 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 expected duration of the mining project 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 |
The expected duration of the mining project in months is
3. The failure data analysis of a longwall mining system consisting of thre major subsystems revealed that the failure rate of shearer, face conveyor any stage loader are 0.15/ hour, 0.2/ hour and 0.1/ hour respectively. If all the subsystems must be running for a satisfactory system operation, the reliability of the longwall system for a period of 4 hours is
4. Consider the following linear programming problem:
Maximize z = 3x + 2y
s.t. 3x + 2y ≥ 15
2x + 3y ≤ 6
x ≥ 0, y ≥ 0
The above linear programming problem has
Maximize z = 3x + 2y
s.t. 3x + 2y ≥ 15
2x + 3y ≤ 6
x ≥ 0, y ≥ 0
The above linear programming problem has
5. The variance of failure time (time to failure) of an electric motor in shovel is 1600 hr2. If the failure time follows an exponential distribution. the expected mean time between failure in hr is
6. The unit cost of transportation of a balanced transportation problem is shown below:
Destination →
D1
D2
D3
Supply
Source s
S1
7
3
6
60
S2
5
4
9
60
S3
8
6
7
80
Demand
50
120
30
The transportation cost of the initial basic feasible solution obtained by the North-West corner rule is
| Destination → | D1 | D2 | D3 | Supply | |
|---|---|---|---|---|---|
| Source s | S1 | 7 | 3 | 6 | 60 |
| S2 | 5 | 4 | 9 | 60 | |
| S3 | 8 | 6 | 7 | 80 | |
| Demand | 50 | 120 | 30 | ||
The transportation cost of the initial basic feasible solution obtained by the North-West corner rule is
7. A workshop has four machines for assigning four jobs. Each job can be assigned to only one machine. Estimated processing cost (in Rs.) at each machine to complete each task is given in the table below
Machine
M1
M2
M3
M4
Tasks
T1
61
92
52
72
T2
42
49
69
85
T3
47
59
80
71
T4
65
70
68
72
The minimum value of total processing cost based on an optimal assignment schedules is
| Machine | |||||
| M1 | M2 | M3 | M4 | ||
| Tasks | T1 | 61 | 92 | 52 | 72 |
| T2 | 42 | 49 | 69 | 85 | |
| T3 | 47 | 59 | 80 | 71 | |
| T4 | 65 | 70 | 68 | 72 | |
The minimum value of total processing cost based on an optimal assignment schedules is
8. The probabilistic nature of activity times in PERT network is described by which one of the following distributions?
9. A pumping station in a mine has 4 pumps, P1, P2, P3 and P4 which are connected functionally in parallel configuration as shown in the figure. The individual reliability of the pumps P1, P2, P3 and P4 are 0.80, 0.90, 0.85 and 0.95 respectively. For an effective dewatering operation in the mine denoting system success, at least three pumps should be in operation. The reliability of the system is
