(b)An economy consists of two industries X and Y with each industry
producing a single product.
The table shows the use and production of X
and Y over some fixed period of time.
TO
X
Y
Consumer Demand
FROM
X
70
35
95
Y
40
60
60
(i)
The final demand for A increases by 40 units and B decreases by
25%.
Determine the new total output by the two industries so as to
satisfy the new final demand.
(10
Marks)
Page
2
of
5
Question Three
(a)Given the information below of a project managed by Xcut company.
Activity
Preceeding Activity
Duration (Days)
A

3
B

3
C

7
D
A
1
E
D, J
2
F
B
2
G
C
1
H
E,F,G
1
J
B
1
You are required:
(17 Marks)
(i)
To draw a network diagram for the project
(ii)
Determine the critical path
(iii)
Calculate ES, EF, LS and LF times for each activity.
(b)Briefly discuss the relation between the arrival and the service rate in a
queue.
(3 Marks)
Question Four
(a)Solve the linear programming problem.
(12
Marks)
Page
3
of
5
Minimize: Z = 2x + 3y
Subject to:
3x + y ≥ 15
0.5x + y ≥ 10
x+ y ≥ 13
y ≥4
(b)Solve the following equation using the matrix algebra method.
(5
Marks)
2x + y =1
x + 2y = 1
(c) In quantitative models, what is the difference between feasible solution
and optimal solution?
(2
Marks)
(d)In a network, what is a dummy activity?
(1 Mark)
Question Five
(a)Perform the following
(i)
Find dy/dx if
Y = 1
+ (x
3
+ 2x)
4
(4 Marks)
x
2
Page
4
of
5
(ii)
∫
1
2
(
x
−
x
2
)
dx
(5
Marks)
(b)A service station is open for 24 hours.
During this time customers
arrive at the filling station with a mean of 30 per hour. The service time
has a mean of 3 customers in 5 minutes.
Calculate the
(i)
Mean service (rate) per hour.
(4 Marks)
(ii) Traffic Intensity
(c) Define the term game theory and illustrate THREE types of games.
(5 Marks)
(d)What is the importance of inputoutput analysis is an economy?
(2 Marks)
Page
5
of
5
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 Fall '19
 Economics, Linear Programming, Optimization, 1 J, KENYA METHODIST UNIVERSITY