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?

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

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

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