UNIVERSITY OF SOUTHAMPTON
MANG 1007: Management Analysis
Class 02 Solutions: Dynamics demand, profit and return 1.A firm splits the country into different sales areas. The following table gives the number of salesmen and the profit in each area. Draw a graph of profit against salesmen.
|Area |London |Roseland |SWest |Midlands |North |Scotland |Wales |
|Salesmen |10 |8 |5 |7 |6 |4 |3 |
|Profit (£K) |100 |150 |160 |170 |180 |140 |110 |
What curve best describes this relationship?
First, sort the data by size of number of salesmen.
|Area |Wales |Scotland |SWest |North |Midlands |Roseland |London |
|Salesmen |3 |4 |5 |6 |7 |8 |10 |
|Profit (£K) |110 |140 |160 |180 |170 |150 |100 |
Then plot the graph:
[pic] The data looks as if the amount of profit follows a quadratic function (one turn in the curve) so that the amount of profit increases per salesman up to six salesmen; after this profit decreases.
2. The following data describes the FTSE 100 index since 1985. Plot the graph of the index against time. What sort of curve would best describe the data?
|Date |Close |Date |Close |
|02/01/2008 |6456.3 |02/01/1996 |3759.3 |
|02/01/2007 |6203.1 |03/01/1995 |2991.6 |
|03/01/2006 |5760.3 |04/01/1994 |3491.8 |
|04/01/2005 |4852.3 |04/01/1993 |2807.2 |
|02/01/2004 |4390.7 |02/01/1992 |2571.2 |
|02/01/2003 |3567.4 |02/01/1991 |2170.3 |
|02/01/2002 |5164.8 |02/01/1990 |2337.3 |
|02/01/2001 |6297.5 |03/01/1989 |2052.1 |
|04/01/2000 |6268.5 |04/01/1988 |1790.8 |
|04/01/1999 |5896 |02/01/1987 |1808.2 |
|02/01/1998 |5458.5 |02/01/1986 |1435 |
|02/01/1997 |4275.8 |02/01/1985 |1280.2 |
As in question 1; it helps to arrange the data in order of date, then plot the graph:
[pic] The values appear to be generally increasing but also follow cyclic pattern (rise and fall). This may be described by a combination of two things: a rise and fall pattern on top of a base line which changes with time, e.g. exponentially.
3.Find the log of the FTSE 100 index for each year using the data in the previous question. Plot the log of the FTSE 100 index against time. What sort of curve is obtained?
The rising and fall pattern is less distinct but still there. This is because values of logs are smaller than actual values. There also appears to be a base linear increase in the logs over which the rise and fall is overlaid. This linear increase would have been the baseline exponential in the original data.
4. Draw the graph of ex . Then draw the graph of loge (x). How are the two related?
If y = ex; then lny = x;
The values on the horizontal axis of ex are the same as the values on the vertical axis of ln(x). Thus, the graph of the natural log, ln(x) tells us the value of x for each value of y in the graph of ex: To get lnx from ex, turn…