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
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
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
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
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
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
In an opencast mine, dumpers arrive at a shovel location with an average arrival rate of 12 per/hour. The inter-arrival times of the dumpers follow an exponential distribution. The service times of the shovel also follow an exponential distribution with an average of 3 minute. The average waiting time of a dumper in the queue in minutes is
The feasibility region of an LP problem in variable x and y is given by the following constraints, in addition to the non- negativity constraints.
y ≤ 60; x ≤ 90; x + y ≤ 70
The numbers of corner point feasible solutions for this problem are
A project network comprises five activities as shown below. The activity durations. in days. are as indicated. Crashing of any activity costs Rs. 1000 per day. If the project is crashed to the shortest possible duration without changing the critical path the total crashing coso in Rs. is
In a PERT network, the activities on the critical path are a, b and c. The standard deviations of the durations of these activities are 2, 2 and 1 respectively. The variance of the project duration is
A mining machinery company has four plants at locations A, B, C, and D and three warehouses at destinations X, Y and Z. The number of machine units available at the plants A, B, C and Dare 5, 8, 7 and 14 respectively. The demands at X, Y and Z are 7, 9 and 18 respectively. The unit costs of transportation in rupees as follows:
Destinations
X
Y
Z
Locations
A
20
70
40
B
30
30
10
C
50
40
70
D
10
60
20
The total number of basic variables obtained based on the initial basic feasible solution is
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 idle time of a dumper in the system?
A queue of trucks at a crusher plant hopper is known to be M/M/1 queue. The probability that there is no truck to unload is 0.3. Due to rains the mean service time at the hopper is increased by 30%. As a consequence, the expected number of trucks in the queuing system (including the one possibly unloading) becomes
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 proportion of time the shovel is busy.
