Prelim- Operations Research

Q1. Solve any 2 (15 marks)

1. 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
1. 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.
2. Explain the following concepts:- Duality in LPP, redundancy in graphical, objective function in LPP

Q2. Solve any 2(15 marks)

1.  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.

1. 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 O2-D3 changes from 7 to 6.

1.  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)

1. 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
1. Compute the critical path and time
2. What is the probability that the assignment would be complete in 55 days
3. 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)

1. 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

1. 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)

1. 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.)

1. 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

1. 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 pay-offs 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 X1 S3 X2 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 = C-Z 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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#### vipin0785

Education Qualification: BMS- N M College (University Rank Holder) PGDBM- Sydenham College M Com- College topper Mr Vipin Saboo has been associated with the following institutes as a visiting faculty Lords college, Malad Patkar College, Goregoan Saraf college, Malad Dalmia college, Malad St Andrews College, Bandra Wilson College, Grant Road Thakur college, Kandivili L N College, Kandivili N K College, Malad Dhanukar College, Vile Parle St Xaviers College, Marine Lines Shroff College, Kandivili KES College, Khar Mr.Vipin Saboo also has more than 5 years of industry expertise with corporate like CRISIL, Motilal Oswal Investment Banking and Yes Bank. Mr. Saboo has also published a text book on Logistics and Supply Chain Management for TYBMS Students.

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