Western National Bank is considering opening a drive-through window for customer service. Management estimates that customers wi
ll arrive at the rate of 15 per hour. The teller who will staff the window can service customers at the rate of one every three minutes.
Part 1 Assuming Poisson arrivals and exponential service, find:
Utilization of the teller
Average number in line
Average number in system
Average waiting time in line
Average waiting time in system, including service
Also calculate the probability of not more than three cars making it through the queue and a 95% service level expectation. Determine the actual service level and what can be done to improve it.
Part 1 Assuming Poisson arrivals and exponential service, find:
Utilization of the teller
Average number in line
Average number in system
Average waiting time in line
Average waiting time in system, including service
Also calculate the probability of not more than three cars making it through the queue and a 95% service level expectation. Determine the actual service level and what can be done to improve it.
1 answer:
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Answer:
(i)The units of production of Product A and B (x and y) are the decision variables
(ii)Objective is to maximize profit
(iii)Objective function, Max P=20x+50y
(iv)The Contraints are:
8x+2y500....(i)
2x+5y400.......(ii)
3y180
x>0, y>0
Explanation:
Let the number of Product A=x
Let the number of Product B=y
Each unit of product A requires 8 units of R1 and 4 units of R2.
Each unit of product B requires 2 units of R1, 5 units of R2, and 3 units of R3
The availabilities of resources R1, R2, and R3 are 500, 400, and 180
Since R1 500,
Product A requires 8 units of R1 per production unit
Product B requires 2 units of R1 per production unit
Total Unit of R1 possible is given by the inequality: 8x+2y500....(i)
Since R2 400,
Product A requires 2 units of R2 per production unit
Product B requires 5 units of R2 per production unit
Total Unit of R2 possible is given by the inequality: 2x+5y400....(ii)
Since R3 180,
Product B requires 3 units of R2 per production unit
Total Unit of R2 possible is given by the inequality: 3y180....(iii)
Since the manufacturer also makes a profit of $20 and $50 for products A and B, our objective is to maximize profit
Therefore: Objective function, Max P=20x+50y ......(iv)