Please use the excel format to answer the question.

Question 1: (8 points) Queueing (arrival and service) Copy machine investment: We are trying to estimate the number of copy machine(s) we should install in the basement of State Farm Hall of Business. Copy machines should be available 24/7. Students may walk up at any time of the day or night for copying. Interarrival time for student's arrival at the copy machine(s) is described by the following discrete probability distribution: Interarrival time (in minutes) Probability 1 0.2 2 0.2 N 3 0.2 4 0.25 5 0.15 Based on past data, it can be assumed that the amount of time a student needs to use the copy machine is described by a discrete probability distribution listed below: Copying time (in minutes) Probability 1 0.30 2 0.20 N 3 0.25 4 0.25 Students do not like waiting at the copy machine for their turn to use them. Students don't depart from the queue until they use the machine. Service policy is first-come, first-serve (whoever arrives first at the machine prioritizes using the machine). Suppose that students' time is valued at $10 per hour, i.e., the student could have used the time wasted waiting to do some other work at that wage rate. Each copy machine can be leased at a rate of $10 per day. The cost of the leasing copy machine is ultimately charged to the common student services. Simulate the process for 30 students to determine the best of two choices described below. Your cost analysis is just as important as the simulation. Use only the random numbers provided. Given the above information, answer the following questions. 1. Assume that the university leases one copy machine. What is the total cost of operating the system per day? (this cost includes the cost of time wasted by the students waiting at the copy machine plus the cost of leasing the copy machine). 2. Assume that the university leases two copy machines. What is the total cost of operating the system per day? 3. Which choice is best and why? B LL G H Random Number A B D E 1 Homework-3. 2 Q1: Copy Machine Investment - Simulation 3 Input Data: 4 5 Copying time (min) Probability Cum Prob 1 0.30 7 2 0.20 8 3 0.25 9 4 0.25 10 11 12 Interarrival time (min) Probability Cum Prob 13 1 0.20 14 2 0.20 15 3 0.20 16 4 0.25 17 5 0.15 18 19 20 Goal: Configure the system to minimize the total cost per day 21 22 Alternatives: Install copy machines = 1 or 2 Random Number D E G H A B 1 copy machine scenario, Student IAT AT R# 3 Copy Time Machine ON Machine OFF Wait Time 1 8 2 3 R# 89 79 68 67 35 38 75 4 5 6 7 65 55 70 58 68 3 | 8 17 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 9 15 65 10 92 21 82 11 19 12 31 45 13 70 58 14 34 87 15 35 68 16 38 67 17 65 75 18 55 58 68 45 19 70 D F F H J A 20 B 37 E 70 21 25 19 22 13 23 63 35 87 52 24 25 70 60 62 55 25 26 27 28 89 59 97 51 29 85 30 30 26 1 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 ? Total Waiting Minutes Simulation time = Minutes Cost analysis (Cost/day) # of minutes waited per day = Wait Time/Simulation Time * 24*60 Minutes per day Cost of waiting/day = (# minutes waited per day/60)* 10 = = $ per day Total Cost = Cost of Waiting + Cost of leasing Copier + = per day E F F G H 2 copy machine scenario, J Machine 2 Student R# IAT AT R# Copy Time Machine 1 OFF Vait Time ON ON OFF 9 1 2 35 53 55 99 3 30 4 31 49 5 39 74 6 19 89 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 7 19 23 62 8 9 67 66 93 10 12 33 11 29 62 73 26 12 13 35 95 14 27 94 15 30 99 16 31 49 17 39 74 an 18 90 89 C F H A 19 K E 83 J 19 20 33 16 21 9 65 22 33 81 23 84 76 24 50 65 25 90 51 26 30 77 27 70 14 28 48 22 29 79 50 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 30 9 73 Total Waited Minutes Simulation time = Minutes Cost analysis (Cost/day) # of minutes waited per day = Wait Time/Simulation Time * 24*60 #DIV/0! Minutes per day Cost of waiting/day = (# minutes waited per day/60) * 10 = $ per day H J per day = + A B E 112 Total Cost = Cost of Waiting + Cost of leasing Copier 113 114 115 116 117 Conclusion with specific reason