#### ENG4004 Engineering Project and Operations Management Solution

Table of Contents

## Assignment 2 Operations Management

Description | Marks out of | Wtg (%) | Due date |

Assignment 2 – Operations Management | 200 | 20.00 | 5 Oct 2021 |

Objectives

This assignment addresses the following objectives for the course as outlined in the course specification:

- use a variety of operational research techniques to analyse complex management problems and to synthesise and evaluate possible solutions to these problems.
- Financially assess projects utilising various inputs, types of costs, break even analysis, and the effect of time on the value of money.

Special Instructions

This assignment is to be electronically submitted via Study desk assignment drop-box. Please submit as a generated PDF file or Word file. Do not submit zip files or scanned PDF files.

File name for your assignment may follow the following format:- Student first and second name ENG4004 ASS 2 S2 2021

For example, Bob James ENG4004 ASS 2 S2 2021

This is not critical but helps in sorting student submissions.

### QUESTION 1 (60 marks)

A gardening supply company manufactures two types of mulch bins – the *Compacto *and the *Enviro*. The production of each bin involves a certain amount of moulding, pressing and assembly as indicated below.

Department | Mulch Bin | |

Compacto | Enviro | |

Moulding | 5 hours | 6 hours |

Pressing | 8 hours | 5 hours |

Assembly | 9 hours | 14 hours |

Next month, the company has maximum available capacities of 630 hours for assembly, 300 hours for moulding and 400 hours for pressing. The company has advance orders for 15 *Compacto *mulch bins and for 10 *Enviro *mulch bins and is committed to supplying these next month. The same profit of $6,000 is made from the sale of each mulch bin.

Use a graphical method to find the approximate answers to the following question and then find the exact values mathematically.

- How many
*Compacto*and*Enviro*mulch bins should be manufactured next month to fulfill advance orders and maximize profits? How much profit will be made? (Assume that partially completed mulch bins can be manufactured but that only completed bins can be sold for profit. Bins on advance order have not yet been paid for.)

(40 marks)

- At the optimum production mix for next month, which if any, of the three departments has any excess capacity, i.e. hours available that are not used? Indicate the amount of any excess capacity in hours.

(10 marks)

- If the profit from the sale of each
*Enviro*mulch bin increases from $6,000 to $15,000 because of its appearance on a popular TV gardening show, how would this affect the proposed production mix for the coming month?

(10 marks)

**Solution**

**QUESTION 2 (40 Marks)**

The electricity half hourly maximum demand for an electricity zone substation has been recorded as shown.

Year | Demand (MW) |

1 | 35.50 |

2 | 41.39 |

3 | 40.23 |

4 | 46.02 |

5 | 43.67 |

6 | 51.38 |

7 | 49.28 |

8 | 58.57 |

9 | 58.07 |

10 | 65.38 |

The demand is expected to continue to grow at an exponential rate.

- Calculate the estimated average future annual percentage increase in maximum demand.
- What is the estimated maximum demand in year 15?

### QUESTION 3 (40 Marks)

A government owned corporation is considering two options for the installation of a large piece of equipment.

They have had firm offers from two companies. Either option will meet the requirements of the project.

Company A has offered to supply and install the equipment for a once off amount of

$5,142,000. In the case of the offer by Company A, there will be ongoing maintence needed

which is estimated to cost $41,000, at current prices, payable to a contractor at the end of each year.

Company B has offered to supply and install smaller piece of equipment for $2,965,000 and then upgrade it to the equipment equivalent to that offered by company A at the end of the 8^{th} year at a firm price of $3,742,000. In the case of the offer by Company B, there will be ongoing maintence needed which is estimated to cost $24,000 at current prices, until the equipment is upgraded, payable to a contractor at the end of each year, including the final year. After year 8, the costs will be the same as for Company A.

The cost of capital for the corporation is 8% p.a. Infaltion is estimated to be 1.9% p.a. for the period.

On the basis of a financial comparison, which offer should be accepted?

### QUESTION 4 (40 Marks)

A company which manufactures and sells small electronic devices includes a small dry cell battery with each device. Because of the large quantity of batteries required it buys them in bulk. It is considering buying from a new supplier and is concerned that although the price is low the batteries may be inferior.

They have purchased a trial batch of 500 batteries and have tested a random sample of 10 of them for capacity. The results in milliamp-hours are as follows.

810 | 882 | 909 | 864 | 904 | 936 | 785 | 936 | 927 | 936 |

- On the basis of the sample, what is the mean value of the whole batch? (5 Marks)
- What range of capacities would include 95% of the whole batch? (15 Marks
- What are the 95% confidence limits for the estimate of the mean value? (10 Marks)
- How many would need to be sampled to determine the mean capacity within plus or minus 20 milliamp hours with a 95% confidence limit? (10 Marks)

### QUESTION 5 (20 Marks)

A company uses many of uses many of a particular sized bolt in its operation. These have been satisfactorily supplied from one source for a number of years. Lately it has been noticed that some of the supplied bolts have faulty threads. This costs the company more than the cost of the bolt because the fault does not become apparent until the bolt is being used in the assembly plant. To determine the severity of the problem, a random sample of 100 bolts from the latest batch of 5,000 received have been tested. Of these 100 bolts, 8% were found to be faulty.

What are the 95% confidence limits of the estimate of the number of faulty bolts in the latest batch?