Operations Management homework help. **Unit 8 Problems**

**Instructions**

Work through the problems in Excel. Enter your answers in the following spaces below. Attach your Word file or Excel spreadsheet where indicated. YOU MUST SUBMIT YOUR EXCEL SPREADSHEET OR OTHER WORK IN ORDER TO RECEIVE CREDIT. FAILURE TO SUBMIT THE EXCEL SPREADSHEET OR OTHER WORK WILL RESULT IN A GRADE OF 0.

You will only have access to the problems once. Therefore, complete all of the problems in Excel, and then enter your answers and upload your Excel file.

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Question 1 10 pts

Refer to the diagrams in the book. Determine the critical path and expected project duration for each of the projects. Record the critical path using hyphens, such as 1-2-3-4-5 or A-B-C-D-E.

- critical path expected duration
- critical path expected duration
- critical path expected duration
- critical path expected duration

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Question 2 10 pts

The new director of special events at a large university has decided to completely revamp graduation ceremonies. Toward that end, a PERT chart of the major activities has been developed. The chart has five paths with expected completion times and variances as shown in the table. Graduation day is 16 weeks from now. Assuming the project begins now, what is the probability that the project will be completed before

- Graduation time? (Round to four decimal places.)
- The end of week 15? (Round to four decimal places.)
- The end of week 13? )Round to four decimal places.)

Path |
Expected Duration(weeks) |
Variance |

A | 10 | 1.21 |

B | 8 | 2.00 |

C | 12 | 1.00 |

D | 15 | 2.89 |

E | 14 | 1.44 |

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Question 3 10 pts

A project manager has compiled a list of major activities that will be required to install a computer information system in her firm. The list includes estimated completion times for activities and precedence relationships.

page 777

Activity |
ImmediatePredecessor |
EstimatedTimes (weeks) |

A | – | 2-4-6 |

D | A | 6-8-10 |

E | D | 7-9-12 |

H | E | 2-3-5 |

F | A | 3-4-8 |

G | F | 5-7-9 |

B | – | 2-2-3 |

I | B | 2-3-6 |

J | I | 3-4-5 |

K | J | 4-5-8 |

C | – | 5-8-12 |

M | C | 1-1-1 |

N | M | 6-7-11 |

O | N | 8-9-13 |

End | H, G, K, O |

- Construct a network diagram. You can use either AOA or AON (see Example 5 on page 752 from our book). Make sure this is in your Excel work that you will upload in a separate question.
- If the project is finished within 26 weeks of its start, the project manager will receive a bonus of $1,000; and if the project is finished within 27 weeks of its start, the bonus will be $500. Find the probability of each bonus. (Round to four decimal places.)

Probability of $1000 bonus

Probability of $500 bonus

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Question 4 10 pts

- lambda = 3 customers/hour
- mu = 5 customers/hour
- M = 1

(1) What is the system utilization? (Three decimal places.)

(2) What is the average number of customers waiting for service? (Three decimal places.)

(3) What is the average time customers wait in line for service? (Three decimal places.)

- Repair calls are handled by one repairman at a photocopy shop. Repair time, including travel time, is exponentially distributed, with a mean of two hours per call. Requests for copier repairs come in at a mean rate of three per eight-hour day (assume Poisson). Determine:

(1) The average number of customers awaiting repairs. (Three decimal places.)

(2) System utilization. (Three decimal places.)

(3) The amount of time during an eight-hour day that the repairman is not out on a call. (Two decimal places.)

(4) The probability of two or more customers in the system. (Four decimal places.)

- An average of 18 customers arrive at a service center each hour. There are two servers on duty, and each server can process 12 customers per hour.

(1) What is the system utilization? (Three decimal places.)

(2) What is the average number of customers in the system (waiting plus being served)? (Three decimal places.)

(3) What is the average time customers wait in line for service? (Three decimal places.)

(4) What is the average waiting time for customers who actually have to wait? (Three decimal places.)

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Question 5 10 pts

Many of a bank’s customers use its automatic teller machine to transact business after normal banking hours. During the early evening hours in the summer months, customers arrive at a certain location at the rate of one every other minute. This can be modeled using a Poisson distribution. Each customer spends an average of 90 seconds completing his or her transactions. Transaction time is exponentially distributed. Determine the following:

- The average time customers spend at the machine, including waiting in line and completing transactions
- The probability that a customer will not have to wait upon arriving at the automatic teller machine
- The average number waiting to use the machine

(Three decimal places.)

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Question 6 10 pts

During the morning hours at a catalog sales department, telephone calls come in at the rate (Poisson) of 40 per hour. Calls that cannot be answered immediately are put on hold. The system can handle eight callers on hold. If additional calls come in, they receive a busy signal. The three customer service representatives who answer the calls spend an average of three minutes with a customer.

- What is the probability that a caller will get a busy signal? (
*Hint:*Solve for log*K*or ln*K*using trial and error.) - What is the probability that a customer will be put on hold?

(Four decimal places.)

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Question 7 0 pts

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