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Basaveshwar Engineering College(Autonomous), Bagalkot-02[TEQIP Lead Institute, Govt. Aided Institution, AICTE Recognized, Affiliated to VTU Belgaum]

Department of Management Studies (MBA)

1st AssignmentSem : 02 Sub :: QUANTITATIVE TECHNIQUES Staff : Dr V.S PURANIK

Last date for submission:26-02-2011

I

1,What is Operations Research?

2. Describe the various steps involved in O.R. study.

3. Explain why it may be advantageous to build models to help in solving a decisionproblem.

4. Enumerate, with brief description, some of the techniques of O.R.

5. Discuss the advantages and limitations of O.R.

6. Discuss the significance and scope of O.R. in scientific management.

7. Identify some areas of application of O.R. technique in your organization.

8.Explain with the help of a suitable example, what do you understand by linear

programming.

9. What are the characteristics and limitations of a linear programming problem?

10. What do you understand by graphical method? Give its limitations.

Problem Formulation

1. Jumpin Ltd. has canned apple and bottled juice as its products with profit marginRs. 2 and Rs. 1 respectively per unit. The following table indicates the labour,equipment and material to produce each product per unit.

Bottled Juice CannedApple

Total

Labour (man hours) 3 2 12

Equipment (machine hours) 1 2.3 6.9

Material (unit) 1 1.4 4.9

Formulate the problem specifying the product mix, which will maximize profit withoutexceeding the various levels of resources.

2. The managing director of a small scale company decides to manufacture twoproducts, P1 & P2, each of which is processed in two shops, viz. Machining shop (M)and Finishing shop (F). One unit of P1 takes 15 hours of machining and 24 hours of

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finishing shops. The corresponding requirements for P2 are 25 hours and 11 hoursrespectively in shops. The total available hours per day in M and F shops are 375 and264 respectively. P1 gives a profit of Rs. 18 per unit and P2 Rs. 16 per unit.Formulate the above problem.

3. A company owns two flour mills, A and B, which have different production

capacities for high, medium and flour. This company has entered a contract to supplyflour to a firm every week with at least 12, 8 and 24 quintals of high, medium andlow grade respectively. It costs the company Rs. 1000 and Rs. 800 per day to runmill A and B respectively. On a day, mill A produce 6, 2 and 4 quintals of high,medium and low grade flour respectively. Mill B produce 2, 2 and 12 quintals of high,medium and low grade flour respectively. How many days per week should each millbe operated in order to meet the contract order most economically.

4. Decibel Electronics produces two products A and B that are sold on a weekly basis.The weekly production cannot exceed 25 for product A and 35 for product B. Thecompany employs a total of 80 workers. Product A requires 2 man-weeks of labourwhereas B requires only 1. A gives a profit of Rs. 16 and B Rs. 40. Formulate the

above LPP.

5. A company that produces soft drinks has a contract that requires that a minimumof 80 units of the chemical A and 60 units of the chemical B go into each bottle ofthe drink. The chemicals are available in a prepared mix from two different suppliers.Supplier X1 has a mix of 4 units of A and 2 units of B that costs Rs. 10, and supplierX2 has a mix of 1 units of A and 1 unit of B that costs Rs. 4. How many mixes fromcompany X1 and company X1 should the company purchase to honour contractrequirement and yet minimize cost?

Graphical Method

1. Maximize z = 50x1 + 60x2

subject to

2x1 + x2e 3003x1 + 4x2 e 5094x1 + 7x2 e 812

x1, x2u 0

2. Minimize z = 2x1 + 1.7x2

subject to

0.15x1 + 0.10x2u 1.00.75x1 + 1.70x2 u 7.51.30x1 + 1.10x2 u 10.0

x1, x2u 0

3. Minimize z = x + y

subject to

2x + y u 125x + 8y u 74x + 6yu 24

x, y u 0

4. Minimize z = 2x1 + 3x2

subject to

-x1 + 2x2e 4

x1 + x2 e 6x1 + 3x2 u 9

x1, x2u 0

5. Minimize z = 3x + 4y

subject to

5x + 8y e 20003x + 10y e1000

x, y u 0