Bule Hora University
Masters of Business Administration program
Course: Quantitative Analysis for Business Decision
Practical questions and assignment (20%)
Instruction I: Workout
1. Personal Mini Warehouses is planning to expand its successful Orlando business into Tampa.
In doing so, the company must determine how many storage rooms of each size to build. Its
objective and constrains follow:
Maximize monthly earnings= 50X1 +20X2
Subject to:
2X1+4X2<400 (Advertising budget available)
100X1 +50X2<8,000(Square footage required)
X1
<60(Rental limit expected)
X1 X2>0
Were,
X1=Number of large spaces developed
X2=Number of large spaces developed
(Use graphical method and find minimum Monthly salary with the values of X1 and X2)
2. Peniel House and Furniture manufacturer produces two products: Beds and Chairs. Each unit
of Bed requires 3 hrs in molding unit, 4hrs in painting unit, and 1 hr in finishing. On the other
hand, each unit of Chair requires 3 hrs in molding unit, 2 hrs in the paint shop and 2 hours in
finishing. Each week, there are 210 hrs available in molding, 200hrs in painting, and 120 hrs
in finishing unit. The demand for Beds cannot exceed 40 units per week. Each unit of Bed
contributes Birr 20 to profit, while each unit of chair contributes Birr 30. Determine the number
of units of each product per week to maximize the profit? (Use Graphic Method to solve the
given LP problem).
3. Assignment Problems (select one of your favors from I-III and do it)
I.
A plant manager has four subordinates, and four tasks to be performed. The
subordinates differ in efficiency and the tasks differ in their intrinsic difficulty. This
estimate of the times each man would take to perform each task is given in the
effectiveness matrix below.
A
B
C
D
I
8
13
38
19
II
26
28
19
26
III
17
4
18
24
IV
11
26
15
10
A. How should the tasks be allocated, one to a man, so as to minimize the total man hours?
II. A dairy plant has five milk tankers I, II, III, IV & V. These milk tankers are to be used on
five delivery routes A, B, C, D, and E. The distances (in kms) between dairy plant
and the delivery routes are given in the following distance matrix
I
II
III
IV
V
A
160
130
175
190
200
B
135
120
130
160
175
C
140
110
155
170
185
D
50
50
80
80
110
E
55
35
70
80
105
A. How the milk tankers should be assigned to the chilling centers so as to minimize the
distance travelled?
III. Find solutions for questions under table
4. Transpiration problems (select one and do it)
IV. For the next given transportation problems (this #IV, V or VI);
A. Develop the transportation model
B. Using the North West Corner Method, find the feasible solution for the problem and
Costs
C. Using the least cost Method, find the feasible solution for the problem and Costs
D. Compare and contrast NWC and Least cost approaches of solving transportation model
based on their total costs.
V. Workput based on questions raised in #IV (a-d)
5. Network analysis
6. Post optimality analysis
A. By deploying three major operations (i.e., assembly, display, and warehousing), a company
provides two types of products (R and S) to customers, generating a sales revenue of birr
110 and birr 90 per unit of each product respectively. Each unit of R demands 3 assembly
hours and 8 m3 for warehouse. On the other hand, 5 assembly hours, 1 portable display,
and 5 m3are demanded for 1 unit of product S. the maximum availability of assembly time,
display, and warehousing space is 150 hours, 20 units, and 300m3respectively.The
combined cost of these resources is $60 and $50 for each unit of products R and S
respectively. Consider the following table.
Required: Based on the above information, answer the following
a. Develop/Formulate the standardized model for the LP problem
b. Interpret the elements of the optimal solution properly
c. Identify the shadow prices of the constraints and express them