**Paper, Order, or Assignment Requirements**

** **

For this coursework you are required to solve a problem using Microsoft Excel for assistance. Your solution should be word-processed, including the computer output (pasted in), and submitted electronically.

Your solution should include both the output itself and a concise account of the methods you have used. Where appropriate you should also explain the reasons you have chosen those particular methods.

2) *Individual Coursework Assignment 2*

This assignment is worth 25% of the overall module mark.

Coursework Brief

*For this coursework you are required to solve a problem using Microsoft Excel for assistance. Your solution should be word-processed, including the computer output (pasted in), and submitted electronically.*

*Your solution should include both the **output** itself and a concise account of the methods you have used. Where appropriate you should also explain the reasons you have chosen those particular methods.*

(a) The number of items, *n*, produced each day by an assembly-line worker, *t* days after an initial training period is modelled by

*N(t)* = 160 – 90*e*^{-0.2t}

Where *N*(*t*) is the number of items at time *t.*

(i) Calculate the number of items produced daily

- 1 day after the initial training period
- 3 days after the initial training period
- 5 days after the initial training period

(ii) What is the worker’s daily production in the long run?

(iii) Use Microsoft Excel to help complete the following table:

Number of days elapsed after initial training period | Number of items produced |

1 | |

2 | |

3 | |

4 | |

5 | |

6 | |

7 | |

8 | |

9 | |

10 | |

11 | |

12 | |

13 | |

14 | |

15 | |

16 | |

17 | |

18 | |

19 | |

20 | |

21 | |

22 | |

23 | |

24 | |

25 |

(iv) Using the data above produce a graph of *N(t)* against *t* within Excel and explain why the general shape might have been expected.

(b) A firm’s total cost function is given by the equation

*TC = 50 +0.05Q ^{3}*

The demand function for the good is

- Write down the equations for total revenue and profit. Calculate the break even points.

(ii) Using Microsoft Excel, complete the following table:

Q |
P |
TC |
TR |
Profit |

0 | 70 | 50 | ||

2 | 66 | 50.4 | ||

4 | 62 | |||

6 | 287.2 | |||

8 | 356.4 | |||

10 | ||||

12 | ||||

14 | ||||

16 | 608 | |||

18 | 612 | |||

20 | ||||

22 | ||||

24 | ||||

26 | ||||

28 | 1147.6 | |||

30 | 1400 | -1100 |

From the data, produce a graph of the total revenue, total cost and profit functions on the same graph, showing any break-even points.

(iii) Using the data and graph produced, write estimate the values of Q within which the firm makes a profit; estimate the maximum profit and the value of Q for which profit is maximised. What is the outlook for this firm?

(iv) Using the equation for total revenue, derive the equation for marginal revenue.

(v) Using the graph of TC against Q, identify the fixed costs (FC), and explain the other features of the graph.

(vi) Calculate the quantity which must be sold to maximise total revenue, using the data in (ii) to confirm your result.

(vii) Explain why maximum profit isn’t obtained by reaching maximum revenue.

* *

Key Marking criteria will include:

- Accuracy of the written and numerical solutions
- Appropriateness of the methodology
- Clarity and conciseness of the descriptions of the methodology

Word Limit

The word limit for this individual assignment is 1000 words.

The School of Management’s detailed word-limit policy, including the penalties relating to breaches of the specified word limit, are incorporated into the electronic cover sheet for coursework (available from the Assessment and Feedback folder on the Blackboard site for this module).