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

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