Great University College
Department of Management
Quantitative Analysis Group Assignment 2
 Total Weight 20%
 Assignment will be submitted using both Hard and Soft Copy
 Each procedure, formant and content are evaluated
 Submission Date 23/01/22
 Late submission and plagiarism/ copying of others file will not be
accepted
1. A transportation problem involves the following costs, supply, and demand.
To
From
1
2
3
1
$500
650
400
2
750
800
700
3
300
400
500
4
450
600
550
Supply
12
17
11
10
10
10
10
Demand
a. Find the initial solution using the northwest corner method, the minimum cell cost
method, and Vogel's Approximation Method. Compute total cost for each.
b.Using the VAM initial solution, find the optimal solution using the modified
distribution method (MODI).
2. Oranges are grown, picked, and then stored in warehouses in Tampa, Miami, and
Fresno. These warehouses supply oranges to markets in New York, Philadelphia,
Chicago, and Boston. The following table shows the shipping costs per truckload
($100s), supply, and demand.
To
From
Tampa
New York
9
Philadelphia
14
Chicago
12
Boston
17
Supply
200
Miami
11
10
M
10
200
Fresno
12
8
15
7
200
Demand
130
170
100
150
Because of an agreement between distributors, shipments are prohibited from Miami to
Chicago.
a. Determine the initial solution using the minimum cell cost method and VAM.
b. Solve using MODI.
c. Are there multiple optimum solutions?
3. Steel mills in three cities produce the following amounts of steel:
Location
Weekly Supply (tones)
Bethlehem
130
Birmingham
210
Gary
320
660
These mills supply steel to four cities where manufacturing plants have the following
demand.
Location
Weekly Demand (tons)
1. Detroit
130
1. St. Louis
70
2. Chicago
180
3. Norfolk
240
Shipping costs per ton of steel are as follows
To
From
1
2
3
4
A
14
9
16
18
B
11
8
7
16
C
16
12
10
22
a. Set up a transportation tableau for this problem and determine the initial solution
using NWCM, LCM and VAM.
b. Solve this problem using MODI.
c.Are there multiple optimum solutions?
4. The Bunker manufacturing firm has five employees and six machines, and wants
to assign the employees to the machines so as to minimize cost. A cost table
showing the cost incurred by each employee on each machine is given below.
Machine
Employee
1
A
$12
B
7
C
20
D
14
E
8
F
2
3
10
5
14
3
13
6
20
9
9
7
11
10
4
5
9
10
11
6
7
14
16
8
9
10
10
12
10
Because of union rules regarding departmental transfer employee 3 cannot be
assigned to machine E and employee 4 cannot be assigned to machine B. Solve this
problem, indicate the optimal assignment, and compute total minimum cost.
5. Great university college department of management head has five instructors to be
assigned to four different courses. All of the instructors have taught the courses in the
past and have been evaluated by the students. The rating for each instructor for each
course is given in the following table (a perfect score is 100).
Instructo
1
r
2
3
4
5
A
80
Course
B
75
C
90
D
85
95
85
93
91
90
95
91
92
90
88
80
93
97
91
84
88
The department head wants to know the optimal assignment of instructors to courses
that will maximize the overall average evaluation. The instructor who is not assigned to
teach a course will be assigned to grade exams. Solve this problem using the assignment
method.