Part A (10 marks each )
1. The manufacturer of patent medicines is proposed to prepare a production plan for
medicines A and B. There are sufficient ingredients available to make 20,000 bottles of
medicine A and 40,000 bottles of medicine B, but there are only 45,000 bottles into
which either of the medicines can be filled. Further, it takes 3 hrs to prepare enough
material to fill 1000 bottles of medicine A and 1 hr to prepare enough material to fill
1000 bottles of medicine B, and there are 66 hrs available for this operation. The profit is
Rs. 8 per bottle for medicine A and Rs 7. Per bottle for medicine B.
a. Formulate this problem as an LPP.
b. How the manufacturer schedule his production in order to maximize profit.
2. In a chemical industry, two products A and B are made involving two operations. The
production of B also results in a byproduct C. The product A can be sold at Rs. 3 profit
per unit and B at Rs. 8 per unit. Forecasts show that up to 5 units of C can be sold. The
Company gets 3 units of C for each unit of A and B produced. Forecasts show that they
can sell all the units of A and B produced. The manufacturing time are 3hrs per unit for A
on operation one and two respectively and 4 hrs & 5 hrs per unit for B on operation one
& two respectively. Because the product C results from producing B, no time is used in
producing C. The available times are 18 and 21 hrs of operation 1 & 2 respectively. The
Company question : how much A and B produced keeping C in mind to make the highest
profit. Formulate LP model for this problem.
3. A firm can produce 3 types of cloths, say A, B and C. 3 kinds of wool are required for it,
say red, green, and blue wool. One unt length of type A cloth needs 2 mts of red and 3
mts of blue wool ; One unt length of type B cloth needs 3 mts of red, 2 mts of green and
3 mts of blue wool; and One unt length of type C cloth needs 5 mts of green and 4 mts
of blue wool. The firm has only a stock of 8 mts of red wool, 10 mts of green wool and
15 mts of blue wool. It is assumed that the income obtained from one unit length of type
A cloth is Rs. 3.00, of type B is Rs. 5.00 and of type C is RS. 4.00. Formulate this
problem as L P P to maximize the farmer’s total profit.
4. Write short note on travelling sales men problem. Solve the following problem with
respect to it.
a
b
c
d
e
f
p
x
20
23
27
29
34
q
21
x
19
26
31
24
r
26
28
x
15
36
26
s
25
16
25
x
23
18
t
23
40
23
31
x
10
u
27
18
12
35
16
x
5. Solve the problem using VAM method and check for optimality by MODI method.(20
marks)
A
B
C
D
supply
13
17
11
14
15
12
20
13
2000
6000
p
q
r
18
18
15
12
3000
3000
4000
5000
7000
demand
6. Solve the following assignment problem.
O
7.
P
Q
R
S
T
A
9
22
58
11
19
27
B
43
78
72
50
63
48
C
41
28
91
37
45
33
D
74
42
27
49
39
32
E
36
11
57
22
25
18
F
3
56
53
31
17
28
A manufacturing company has four zones A, B, C, D and four sales engineers P, Q, R S
respectively, for assignment. Since the zones are not equally rich in sales potential, it is
estimated that a particular engineer operating I na particular zone will bring the following
sales.
Zone A : 4,20,000, Zone B:
Zone C: 2,94,000, Zone D:
3,36,000
4,62,000
The criteria of maximum expected total sales is to be met by assigning the best engineer to the
richest zone, the next best to the second zone and so on. Find the optimal assignment and
maximal sale.
a
b
c
d
p
140
112
98
154
q
90
72
63
99
r
110
88
77
121
s
80
64
86
88
8.
The owner of a fancy goods shop is interested to determine how many advertisements to
release in the selected three magazines. A, B, and C. His main purpose is to advertise in such
a way that total exposure to principal buyers of his goods is maximized. Percentages of
readers for each magazine are known. Exposure in any particular magazine is the number of
advertisements released multiplied by the number of principal buyers. The following data are
available.
Particulars
A
Magazines
b
C
Readers
Principal
buyers
Cost per Adv
1.0 lakh
.6
lakh
0.4 lakh
20%
8,000
15%
6,000
8%
5,000
The
budget
amount is at most Rs.
1.0 lakh for the advertisements. The owner has already decided that magazine A should
have no more than 15 advertisements and that B and C each gets at least 8 advertisements.
Formulate a LPP model for this problem.
9. Evening shift resident doctors in Govt. Hospital work five consecutive days and have 2
consecutive days off. Their 5 days of work start on any day of the week and the schedule
rotates indefinitely. The hospital requires the following minimum number of doctors
working.
Sun Mon Tue Wed Thu Fri
Sat
35
55
60
50
60
50
45
No more than 40 doctors can start their five working days on the same day. Formulate the
general linear programming model to minimize the number of doctors employed by the
hospital.
10. The Omega Data Processing company performs three types of activity : pay rolls, account
receivables, and inventories. The profit and time requirements for key punch computation
and office printing for a standard job are shown in the table below.
Omega guarantees over night completion of the job. Any job schedule during the day can
be completed during the day or night. Any job scheduled during the night, however ,
must be completed during the night. The capacity for both day and night is shown in the
following table:
Capacity Key punch Computation Print
Day
Night
4,200
9,200
150
250
400
650
Formulate the linear programming problem in order to determine the ‘mixture’ of
standard jobs that should be accepted during the day and night.
11. Define Operation Research. List out the applications and limitations of OR.
12. Explain the characteristics and phases of OR.
Part B ( 5 marks each)
13. Write different steps in Hungarian algorithm to solve an assignment problem.
14. Define:
i)
ii)
iii)
iv)
v)
Transportation problem
Feasible solution
Basic feasible solution
Optimum solution
Unbalanced assignment problem
15. Solve the following assignment problem :
a
b
c
p
10
7
8
q
8
9
7
r
7
12
6
s
10
10
8
16. Old hens can be bought at Rs. 2 each and young hens at Rs. 5 each. The old hens lay 3 eggs
per week and the young ones lay 5 per week, each egg being worth 30 paise. A hen (old or
young) cost Rs.1 per week to feed. I have only Rs.80 to spend for hens, how many of each kind
should I buy to give a profit more than Rs. 6 per week, assuming that I cannot house more than
20 hens. Formulate LPP for the above problem and plot the graph.
17. Solve graphically : Max Z =3x1 + 2x2 subject to constraints: x1-x2<=1, x1+x2 >=3 and
x1,x2 >=0.
18. Solve graphically : Min Z =1.5x1 +2.5x2 subject to constraints: x1+3x2>=3, x1+x2>=2
and x1 & x2 >0.
19. Max Z=-x1+2x2 sub to constraints: -x1+2x2<=4, and x1, x2 >=0. Solve graphically.
20. Max Z=-3x1+2x2 sub to constraints: x1<=3, x1-x2<=0 and x1,x2>=0. Solve graphically.