P. R. Pote (Patil) Education & Welfare Trust's Group of Institutions
College of Engineering & Management, Amravati
Department of Mechanical Engineering
B.E. Final Year
(Sem: VIII ) S- 2024
Max. Marks:- 30
Assignment-Unit I
Sub: ORT
(Code:- 8ME04)
Date:- 31/01/24
Instructions to candidates:
(1) All questions are compulsory
(2) Draw neat and labeled diagram wherever necessary.
(3) Due credit will be given to neatness and adequate dimensions.
(4) assume suitable data wherever necessary.
Q.1
Define Operation Research and what are various phases of Operation Research?
Explain also Different models of Operation research.
Q.2
Suppose an organisation is manufacturing two products P1and P2. The profit per
tonne of the two products are Rs. 50 and Rs. 60 respectively. Both the products
require processing in three types of machine. The following Table indicates the
available machine hours per week and the time required on each machine for
one tonne of P1 and P2. Formulate this product mix problem in the linear
programming and solve it graphically.
Table Showing the available machine capacities
And machine hour requirement of two products
Machine1
Machine 2
Machine 3
Q.3.
Product 1
(time)
2
3
4
Product 2
(time)
1
4
7
CO
1
BL
2
Marks
10
1
4
10
1
4
10
Total available machine
hours/weeks
300
509
812
A company buying scrap metal has two types of scrap metal available to him. The
first type of scrap metal has 30% of metal A, 20% of metal B and 50% of metal C
by weight. The second scrap has 40% of metal A, 10% of metal B and 30% of
metal C. The company requires at least 240 kg. of metal A, 100 kg. of metal B
and 290 kg. of metal C. The price per kg. of the two scraps are Rs. 120 and Rs.
160 respectively. 'Determine the optimum quantities of the two scraps to be
purchased so that the requirements of the three metals are satisfied at a
minimum cost. (Formulate and solve)
P. R. Pote (Patil) Education & Welfare Trust's Group of Institutions
College of Engineering & Management, Amravati
Department of Mechanical Engineering
B.E. Final Year
(Sem: VIII ) S- 2024
Max. Marks:- 30
Assignment-Unit 2
Sub: ORT
(Code:- 8ME04)
Date:- 31/01/24
Instructions to candidates:
(1) All questions are compulsory
(2) Draw neat and labeled diagram wherever necessary.
(3) Due credit will be given to neatness and adequate dimensions.
(4) assume suitable data wherever necessary.
CO
2
BL
3
Marks
10
Q.1
Five salesmen are to be assigned to five districts. Estimates of sales revenue (in
thousands) for each salesman are given as follows:
A
B
C
D
E
1
32
38
40
28 40
2
40
24
28
21 36
3
41
27
33
30 37
4
22
38
41
36 36
5
29
33
40
35 39
Find the assignment pattern that maximises the sales revenue. (maximization
model)
Q.2
A company is producing a single product and selling it through five agencies
situated in different cities. All of a sudden, there is a demand for the product in
five more cities that do not have any agency of the company. The company is
faced with the problem of deciding on how to assign the existing agencies to
dispatch the product to the additional cities in such a way that the travelling
distance is minimised. The distances (in km) between the surplus and deficit
cities are given in the following distance matrix. (minimization model)
Deficit City
I
II
III
IV
V
Surplus
A
32
38
40
28 40
City
B
40
24
28
21 36
C
41
27
33
30 37
D
22
38
41
36 36
E
29
33
40
35 39
Determine the optimum assignment schedule
2
4
10
Q.3.
To stimulate interest and provide an atmosphere for intellectual discussion, the
faculty of mathematical sciences in an institute decides to hold special seminars
on four contemporary topics – Statistics, Operations Research, Discrete
Mathematics, Matrices. Each such seminar is to be held once a week. However,
scheduling these seminars (one for each topic and not more than one seminar
per day) has to be done carefully so that the number of students unable to
attend is kept to a minimum. A careful study indicates that the number of
students who cannot attend a particular seminar on a specific day is as follows:
2
4
10
Statistics Operation Discrete Matrices
Research
Math
Monday
50
40
60
20
Tuesday
40
30
40
30
Wednesday
60
20
30
20
Thursday
30
30
20
30
Friday
10
20
10
30
Find an optimal schedule for the seminars. Also find the number of students
who will be missing at least one seminar.(Unbalanced Model)
Q.4
Obtain an initial basic feasible solution to the following transportation problem
by Vogel Approximation method and Check optimality by Modified Distribution
Method.
D1
D2
D3
D4
Supply
S1
19
30
50
10
7
S2
70
30
40
60
9
S3
40
8
70
20
18
Demand
5
8
7
14
2
4
10