Prelim Operations Research
Q1. Solve any 2 (15 marks)
 A company manufactures and sells 3 varieties of pressure cookers. Supply of aluminium is limited to 750 kgs per week and the machine is available for 600 hours per week. The resource usage and profitability of each model is given as follows. Formulate and solve by simplex
Model 1  Model 2  Model 3  
Aluminum  6  3  5 
Machine  3  4  5 
Contribution  60  20  80 
 A company manufactures two products A and B. Profit per unit of A and B are Rs 3, 5 respectively. Each unit of A and B requires 3 and 2 units of labour hours. The company has a maximum of 18 labour hours available. Also the maximum demand for A and B is limited to 4 and 6 units respectively. Formulate the above as LPP and solve by Graphical.
 Explain the following concepts: Duality in LPP, redundancy in graphical, objective function in LPP
Q2. Solve any 2(15 marks)
 Consider the problem of assigning 4 clerks to 4 tasks. Time in hours taken by each is given below.
Tasks  
Clerks  A  B  C  D 
I  4  7  5  6 
II  3  8  7  4 
III  3  5  5  3 
IV  6  6  4  2 
Clerk II cannot be assigned A and Clerk III cannot be assigned B. Find the optimum allocation. How do you find out that an alternate solution exists in the assignment sum.
 The following transportation sum is solved and given
D1  D2  D3  D4  SUPPLY  
O1  5  10  4 (100)  5  100 
O2  6 (200)  8  7  2 (50)  250 
O3  4 (50)  2 (100)  5 (50)  7  200 
DEMAND 
250  100  150  50 

Is the above solution optimum. What would the new solution be if cost from O2D3 changes from 7 to 6.
 Find IFS by VAM and verify by MODI.
W1  W2  W3  W4  Capacity  
A  21  16  25  13  1100 
B  17  18  14  23  1300 
C  32  27  18  41  1900 
Demand  600  1000  1200  1500 
Q 3. Q 5. Solve any 2(15 marks)
 The data pertaining to a project is given below
Activity  Preceeding activity  Optimistic time  Most likely time  Pessimistic time 
A  –  4  6  8 
B  A  5  7  15 
C  A  4  8  12 
D  B  15  20  25 
E  B  10  18  26 
F  C  8  9  16 
G  E  4  8  12 
H  D,F  1  2  3 
I  G,H  6  7  8 
 Compute the critical path and time
 What is the probability that the assignment would be complete in 55 days
 What number of days has the probability of covering the task in 90 percent
(area under 2.29= 0.4890 and area under 1.28= 0.40)
 For the following activity compute ES, EF, LS, LF and TF and the critical path
Activity  Predecessor  Duration 
A  None  3 
B  None  8 
C  B  6 
D  B  5 
E  A  13 
F  A  4 
G  F  2 
H  C,E,G  6 
I  F  2 
 The following information is available for a network. Indirect cost id Rs 300 per day. Time give is in days
Job  1—2  1–3  2—3  2–4  2–5  3–6  4–5  5–6 
Normal time  9  15  7  7  12  12  6  9 
Normal cost  1300  1000  1000  1200  1700  600  1000  900 
Crash time  4  13  4  3  6  11  2  6 
Crash cost  2400  1380  1540  1920  2240  700  1600  1200 
Draw the network diagram and find the critical path and corresponding cost. What would be the impact on the cost if the deadline of 27days is imposed?
Q4. Solve any 2( 15 marks)
 Define: Game, Saddle point, FIND OPTIMUM strategy for A and B
B1  B2  B3  
A1  4  2  1 
A2  3  4  2 
A3  3  4  2 
(2.5 marks each.)
 Prepare a sequencing schedule and find out idle time on machine M1 and M2. Time in days
Job JI J2 J3 J4 J5
M1 3 7 4 5 7
M2 6 2 7 3 4
 The research department of Hindustan Unilever has recommended to the marketing department to launch a shampoo of three different types. The marketing manager has to decide about the type of shampoo to be launched under the following estimated payoffs for various levels of sales:
Types of shampoo  Estimated levels of sales  
15000  10000  5000  
Egg shampoo  30  10  10 
Clinic Shampoo  40  15  5 
Delux shampoo  55  20  3 
What will be the marketing manager’s decision if:
Maximin ii) Maximax iii) Laplace and iv) Minimax (Regret) criterion is applied
Q 5. Zigma Electronics produces two models of electronic products using Resistors, Capacitors and Chips.
Resource  Unit resource requirement  Maximum Availability  
Model 1  Model 2  
Resistor
Capacitor Chips 
2
2 0 
3
1 4 
1200
1000 800 
Unit profit (Rs).  3  4 
After formulating the above problem as a Linear Programming Problem the following optimal Simplex Solution table is obtained.
Profit
Coefficient 
Basis
Variables 
Solution
Values 
3  4  0  0  0  
_{X1}  _{X2}  _{S1}  _{S2}  _{S3}  
C  X  B  
3
0 4 
X_{1}
S_{3} X_{2} 
450
400 100 
1
0 0 
0
0 1 
1/4
2 _{1/3} 
¾
2 1/2 
0
1 0 

Z  3  4  7/12  ¼  0  
= CZ  0  0  7/12  1/4  0 
 Is the solution optimum (2 marks)
 What is the product mix and optimum profit (2 marks)
 Determine the worth of each resource.(1 mark)
 Is the solution degenerate. (2 marks)
 Is the solution unique(2 marks)
 How much of percentage of each resource is left( 3 marks)
 If a new product is launched, that uses 4 units of each resource, what should be the minimum contribution so that you can launch it. (3 marks)
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