MCA
QTD 300
ASSIGNMENT 2
Answer all questions
QUESTION ONE
A) A manufacturing company produces mango juice and yoghurt with a contribution of MK8
and MK10 per unit respectively. The production data are as follows:
Labour hours
Material Mango Juice
Material Yoghurt
4
5
7
Mango Juice
6
3
9
Yoghurt
500
350
800
Total available
Required
i. Formulate the Linear Programming model.
ii. Solve the model using the graphical method
(10 marks)
(10 marks )
B) A firm produces three products X, Y Z with a contribution of K20, K18, and K36
respectively. Production data is as follows:
Product
X
Y
Z
Availability
Machine hours
5
3
6
3000 hrs
Labour hours
2
5
3
2500 hrs
Required
i. Set up the initial Tableu including the necessary slack variables
ii. Solve this LP using the simplex method
iii. Using the tables indicate the shadow prices
Material Kgs
8
10
3
10000 Kg
(5 marks)
(10 marks )
(5 marks)
C) Graphically analyse the following problem:
Maximise profit =
Subject to
i)
ii)
K4X + K6Y
X + 2Y ≤ 8 hours
6X + 4Y ≤ 24 hours
What is the optimal solution
(15 Marks)
If the first constrain is altered, does the feasible region or optimal solution
change?
(5 Marks)
QUESTION TWO
A) Time taken to complet jobs of a particular type is known to be normally distributed with
mean 6.2 hours and standard deviation 1.1 hours. What is the probility that a randomly
selected jobs of this type takes:
i.
ii.
iii.
Less than 7.2 hours
Less than 5.9 hours
Between 5.9 hours and 7.2 hours
(5 marks)
(5 marks )
(5 marks)
B) The output of two secretaries of the CEOs was compared over a number of days with the
following results:
Secretary A
Secretary B
Mean Output
30
32
Standard Deviation
6
5
Required
i. Is there significance in output at 5 percent level?
ii. Is there significance in output at 1 percent level?
iii. What can you say about the results you have calculated?
Days Observed
50
60
(5 marks)
(5 marks )
(5 marks)
C) The management of a company claims that the average weekly earnings of their employees
is MK450. A shop steward disputes this figure, beleiving that the average earnings are
somewhat lower. In order to test this claim, a random sample of 150 employees is selected
from the pay roll and their gross pay noted. The sample results show an average of K428,
with a standard deviation of K183.13. Use an appropriate significance test at 5 percent level
to define which side of this agrument you agree with.
(10 Marks)