TUTORIAL ONE
LINEAR PROGRAMMING
A manufacturer produces two models of racing bike B and C, each of which must be
processed through two machine shops. Machine shop 1 is available for 120 hrs per month and
machine shop 2 for 180 hrs per month. The manufacturer of each bike of type B takes 6 hrs in
shop 1 and 3 hrs shop 2. The corresponding times for C are 4 and 10 hours respectively. If the
profit is $180 and $220 per bike respectively.
Required:
i) Formulate the linear programming model which maximizes profit.
(5)
ii) Solve this model graphically and determine how many bikes of type B and C are produced
in order to maximize profit.
(20)
TUTORIAL TWO
INDEX NUMBERS
a) Define an Index Number as used in business statistics
(2)
b) Identify any four factors that need to be considered when designing an index number (4)
c) The following are prices in dollars and quantities of six food items consumed by a typical
family in 2013 and 2014
Item
Bread
Rice
Eggs (Dozen)
Milk(500ml)
Sugar
Coffee
Price($) (2013)
0.87
1.05
1.05
2.94
0.86
3.43
Quantity in
Units (2013)
50
26
102
30
40
12
Price($) (2014)
1.28
2.17
3.87
1.16
2.54
3.68
Quantity in
Units (2014)
55
20
130
40
41
12
Required
Using year 2013 as base year, calculate:
i) the Laspeyres indices for 2014 and comment on your results
ii) the Paasche indices for 2014 and interpret on your findings
iii) the Fishers ideal index for 2014 and report on your results
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(6)
(7)
(7)
TUTORIAL THREE
REGRESSION AND CORRELATION ANALYSIS
a) State any four uses of regression analysis in business management
(4)
b) The training manager of a company that assembles and exports pool pumps wants
to know if there is a link between the number of hours spent by assembly workers in
training and their productivity on the job. A random sample of 10 assembly workers
was selected and their performances evaluated.
Training Hours
Output
20
40
36
70
20
44
38
56
40
60
33
48
32
62
28
54
40
63
24
38
Required:
(i) Construct a scatter plot of the sample data and comment on the relationship between hours
of training and output.
(5)
(ii) Calculate a simple regression line, using the method of least squares method, to identify a
linear relationship between the hours of training received by assembly workers and their
output.
(8)
(iii) Calculate the coefficient of determination between training hours received and worker
output. Interpret its meaning and advise the training manager.
(5)
(iv) Estimate the average daily output of an assembly worker who has received only 25 hours
of training.
(3)
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