A self-service store employs one cashier at its counter. 9 customers arrive on an average every 5 minutes while the cashier can serve 10 customers in 5 minutes. Assuming Poisson distribution for arrival rate and exponential distribution for services, find i) Average number of customers in the system, ii) Average length of the queue, iii) Average time a customer spends in the system, and iv) Average time a customer waits before being served.
A tourist car operator finds that during the past few months the car's use has varied so much that the cost of maintaining the car has varied considerably. During the past 200 days the demand for the car fluctuated as below:
Using random numbers, simulate the demand for a 10-week period.
What is operations research? Why operations research is important in the field of Mechanical Engineering?
Alumco manufacturers Aluminum sheets and Aluminum bars. The maximum production capacity is estimated at either 800 sheets or 600 bars per day. The maximum daily demand is 550 sheets and 560 bars. The profit per ton is $40 per sheet and $35 per bar. Formulate the problem as a linear programming problem.
Use graphical method to solve the following problem
Maximizez=2x1+3x2Maximize \quad z = 2x_1 + 3x_2Maximizez=2x1+3x2
Subject tox1+x2≤1Subject \ to \quad x_1 + x_2 \le 1Subject tox1+x2≤1
3x1+x2≤43x_1 + x_2 \le 43x1+x2≤4
x1,x2≥0x_1, x_2 \ge 0x1,x2≥0
The arrival rate of customers at a banking counter follows Poisson distribution with a mean of 45 per hour. The service rate of the counter person also follows Poisson distribution with a mean of 60 per hour. What is the probability of having 0 customers in the system? P5P_5P5 Find LsL_sLs, LqL_qLq, wsw_sws and wqw_qwq.
A tourist operator finds that during the past few month the car's uses has varied so much that the cost of maintaining the car has varied considerably. During the past 200 days the demand for the car fluctuated as below