FULLY EXPLANATION

QUESTION ONE

Write down short notes on:

Final demand. (2marks)

Technical coefficients. (2marks)

Closed model versus open model. (3marks)

Three industries, packaging P, Bakery B, and Flour F are related with the intermediate demand matrix below.

Output industry

Input Industry

The final demand for P, B and F are:

D =

Required:

Determine the total output for products of industries P, B and F. (10 marks)

Comment on the total output for industries. (3 marks)

QUESTION TWO

Define the following terms as used in measures of dispersion:

Platykurtic versus leptokurtic and mesokurtic. (6marks)

Coefficient of skewness. (2marks)

Quartile deviation. (2marks)

b) A survey by Marketing Society here in Kenya found out the following buying habits of household air conditioners considered a luxury.

Gross income per month	Number of consumers who buy Air conditioner
Up to 5,000	2
5,001 - 10,000	15
10,001 - 15,000	25
15,001 - 20,000	28
20,001 - 25,000	33
25,001 - 30,000	35
30,001 - 35,000	38
35,001 and above.	40

Required:

Calculate the arithmetic mean, median and mode. (5 marks)

Does the survey show that the luxury item is consumed by high-income earners? Show your answer by calculating appropriate measure of skewness. (5 marks)

QUESTION THREE

In connection with probability, define the following terms

Compound event (2 marks)

Mutually exclusive events (2 marks)

Collective exhaustive events (2 marks)

Equally likely events (2 marks)

Conditional probability (2 marks)

Given the following distribution of wages for 500 technicians in motor companies in industrial area.

Wages in KSh	3000-4000	4000-5000	5000-6000	6000-7000	7000-8000	8000-9000
No. of technicians	30	40	250	100	60	20

A technician is chosen from the above group. What is the probability that his wages are?

Under KSh 5,000 (4 marks)

Above KSh 6,000 (4 marks)

Between KSh 5,000 and KSh 6,000 (2 marks)

QUESTION FOUR

Define the goodness of fit test. How is it applied in accounting? (5 marks)

A research studying the role of stress and its implication on personal life in respect of job change over by low cadre staff, came up with the following data. It relates to 30 firms over 3-year period

No. of people changing jobs in a year	0	1	2	3	4	5	6	7	8	9
Observed frequency	8	18	19	20	16	12	8	4	3	2

By fitting a Poisson distribution to get expected frequency, test its goodness of fit. (15 marks)

QUESTION FIVE

With reference to linear regression define the following terms:

Scatter diagram.

Bivariate distribution.

Positive correlation.

Confidence interval.

Auto correlation. (10 marks)

The following data relates business turnover and staff of fast moving consumer goods company EAI Ltd:

Year	1993	1994	1995	1996	1997	1998	1999	2000
Business turnover in Millions of shillings	45	50	60	75	80	110	150	170
Staff	2,600	3,000	3,100	3,530	3,850	4,300	5,870	7,150

Required:

Fit an appropriate regression equation. (8 marks)

Estimate the staff requirement when business turnover reaches Sh.200 Million. (2 marks)

SECTION II

QUESTION SIX

What are the underlying assumptions in linear programming? (5 marks)

Zadock ltd. manufactures various kinds of furniture namely ordinary chairs, baby cots, and executive chairs. All the products use raw material (wood), machine time (lathe) and manual labour (technicians).

The requirements for the furniture are summarised as below.

	wood in Cubic meters	Lathe time in hours	Technician time in hours
Ordinary chair	10	3	2
Baby cots	12	5	3
Executive chairs	20	6	5

The estimated profits for each kind of furniture are Sh. 26, Sh. 35 and Sh. 50 respectively. There is a limitation of capacity, in that only 300 cubic meters of wood, 118 hours of lathe time and 90 hours of technician time are available.

This problem was solved using a spreadsheet and the following was obtained.

Target Cell (Max)
Name	Final Value
Z	856
X1	6
X2	20
X3	0
Constraints
Name	Cell Value	Status	Slack
wood	300	Binding	0
lathe	118	Binding	0
technician	72	Not Binding	18
X1	6	Not Binding	6
X2	20	Not Binding	20
X3	0	Binding	0
Variables
	Final	Reduced
Name	Value	Gradient
X1	6	0
X2	20	0
X3	0	-2

Constraints
	Final	Dual
Name	Value	Price
wood	300	1.78571428
lathe	118	2.71428571
technician	72	0
Coefficients
Adjustable	Lower	Target	Upper	Target
Name	Value	Limit	Result	Limit	Result
X1	6	-3.5972E-14	700	6	856
X2	20	0	156	20	856
X3	0	0	856	0	856

Required:

Formulate the linear programming problem into standard form for input to the computer spreadsheet (5 marks)

What are the units of each kind of furniture to be produced to maximise profits. What is the maximum profit? (5 marks)

Is there any resource that is not used up? For the used up resource if any, how much would you pay for one additional unit. (5 marks)