BSc (Hons) Business Information Systems
Cohort BIS / 06 / Part Time and BIS / 07 / Full Time
Examinations for 2008 - 2009 / Semester 2
MODULE: BUSINESS DECISION MAKING TECHNIQUES
MODULE CODE: MATH 2111
Duration: 2 Hours 30 Minutes
Instructions to Candidates:
1. Answer ANY FOUR questions.
2. Questions may be answered in any order but your answers must show
the question number clearly.
3. Always start a new question on a fresh page.
4. All questions carry equal marks.
5. Graph papers are attached.
6. Total marks 100.
This question paper contains 5 questions and 5 pages.
Page 1 of 5
Question 1: (25 Marks)
(a) A firm can produce three types of cloth: A, B and C. Three kinds of
wool are required for it: red wool, green wool and blue wool. One unit
length of type A cloth needs 2 meters of red and 3 meters of blue wool.
One unit length of type B cloth needs 3 meters of red wool, 2 meters
of green wool and 2 meters of blue wool and one unit length of type
C cloth needs 5 meters of green and 4 meters of blue wool. The firm
has in stock: 8 meters of red wool, 10 meters of green wool and 15
meters of blue wool. It is assumed that the income obtained from one
unit length of type A cloth is $3, of type B cloth is $5 and that of type
C is $4. Formulate the problem as a linear programming problem to
maximize the income from the finished cloth.
[10 marks]
(b) Use the graphical method to solve the linear programming problem
Maximize
Z = 7x1 + 5x2
subject to the constraints
3x1 + 4x2 ≤ 240
2x1 + x2 ≤ 100
x2 ≤ 45
x1 ≥ 10
with x1 , x2 ≥ 0.
[15 marks]
Question 2: (25 Marks)
(a) Define the following terms associated with the Simplex method
(i) Pivot column.
(ii) Minimum ratio rule.
[2 + 3 = 5 marks]
(P.T.O)
Page 2 of 5
(b) Use the Big-M simplex method to solve the linear programming problem
Minimize
Z = −3x1 + x2 + x3
subject to the constraints
x1 − 2x2 + x3 ≤ 11
−4x1 + x2 + 2x3 ≥ 3
2x1 − x3 = −1
with
x1 , x2 , x3 ≥ 0.
[20 marks]
Question 3: (25 Marks)
Powerco has three electric power plants P1, P2 and P3 that supply the needs
of four cities C1, C2, C3 and C4. Each power plant can supply the following
number of kilowatt-hours (kwh) of electricity: P1 - 35 million, P2 - 50 million
and P3 - 40 million. The power demand (in kwh) in the four cities are: C1
- 45 million, C2 - 20 million, C3 - 30 million and C4 - 30 million. The costs
of sending 1 million kwh of electricity (in million dollars) from plant to city
are given in Table 1.
P1
From P2
P3
Demand (in million kwh)
C1
8
9
14
45
To
C2 C3
6 10
12 13
9 16
20 30
C4 Supply (in million kwh)
9
35
7
50
5
40
30
Table 1: Shipping costs, Supply and Demand of Powerco
(a) Find the initial basic feasible solution using the North-West Corner Rule.
(b) Determine the optimal solution to the problem to minimize the total
shipping cost.
[6 + 19 = 25 marks]
Page 3 of 5
Question 4: (25 Marks)
(a) State and prove the weak duality theorem.
[6 marks]
(b) The Dakota Furniture Company manufactures desks, tables and chairs.
The manufacture of each type of furniture requires lumber and two
types of skilled labor: finishing and carpentry. The amount of each
resource needed to make each type of furniture is given in Table 2.
Resource
Lumber (board ft)
Finishing hours
Carpentry hours
Desk Table Chair
8
6
1
4
2
1.5
2
1.5
0.5
Table 2: Resource requirements for Dakota Furniture
Currently, 48 board ft of lumber, 20 finishing hours and 8 carpentry
hours are available. A desk sells for $60, a table for $30 and a chair for
$20. Dakota believes that the demand for desks and chairs is unlimited,
but at most five tables can be sold. Because the available resources have
already been purchased, Dakota wants to maximize total revenue.
(i) Write the DUAL of Dakota problem.
(ii) Suppose an entrepreneur wants to purchase all of Dakota’s resources. Then the entrepreneur must determine the price he is
willing to pay for a unit of each of Dakota’s resources. Give an
economic interpretation of the DUAL problem.
[10 + 9 = 19 marks]
Question 5: (25 Marks)
(a) MachineCo has 4 machines and 4 jobs to be completed. Each machine
must be assigned to complete one job.
(P.T.O)
Page 4 of 5
The time required to set up each machine for completing each job is
shown in Table 3.
Machine
M1
M2
M3
M4
Job
J1 J2 J3 J4
14 5
8
7
2 12 6
5
7
8
3
9
2
4
6 10
Table 3: Data for MachineCo problem
Determine how should the jobs be allocated to minimize the total time?
[12 marks]
(b) A company is contemplating whether to produce a new product. If it
decides to produce the product, it must either install a new division
which will cost $4 million or work overtime with overtime expenses of
$1.5 million. If the company decides to install a new division, it needs
the approval of Government and the company feels that there is a 70%
chance of getting the approval.
Table 4 reveals the following facts on the sales’ magnitude for the new
product.
Sales Magnitude
High
Medium
Low
Nil
Probability Profit(million $)
0.45
15
0.30
7
0.20
3
0.05
-5 (Loss)
Table 4: Data on the sales of new product
By resorting to overtime, the company will not be in a position to meet
the High sales magnitude. It will be able to satisfy up to the level of
Medium magnitude only, even if High magnitude of sales results. Solve
this problem in order to suggest which option should the company
select.
[13 marks]
***END OF QUESTION PAPER***
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MATH 2111
ID Number.:...................................
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MATH 2111