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Sri Balaji College of Engineering and Technology, J aipur

Department of Mechanical Engineering

Session (2011-12)

B.Tech. IV Year/VII Semester Subject: - Operations Research

Branch: - Mechanical Engineering Date of assignment: - 22/09/2012

Prepared by: - Mr. Deepak Agrawal Date of submission: - 25/09/2012

Assignment No. 01 (Unit-I)

1. A factory manufactures two productsA and B on three machinesX,Y, and Z. Product Arequires 10 hours of machine X and 5 hours of machineY a one our of machineZ. The

requirement of product B is 6 hours, 10 hours and 2 hours of machine X,Y and Zrespectively. The profit contribution of products A andB are Rs. 23/ per unit and Rs. 32/ per unit respectively. In the coming planning period the available capacity of machinesX,Y and Z are 2500 hours, 2000 hours and 500 hours respectively. Find the optimalproduct mix for maximizing the profit.

2. A patient visits the doctor to get treatment for ill health. The doctor examines the patientand advises him to consume at least 40 units of vitaminA and 50 units of vitaminBdailyfor a specified time period. He also advises the patient that to get vitaminAand vitaminBhe has to drink tonic X and tonicY that have both vitamin A and vitamin B in aproportion. One unit of tonic X consists 2 units of vitamin A and 3 units of vitamin Band one unit of tonicY consists of 4 units of vitamin A and 2 units of vitamin B. These

tonics are available in medical shops at a cost of Rs.3.00 and Rs.2.50 per unit of X andYrespectively. Now the problem of patient is how much ofX and how much ofY is to bepurchased from the shop to minimise the total cost and at the same time he can getrequired amounts of vitamins A and B.

3. University professors sometimes engage in businesses to make a little extra cash.Professor Snape and his family run a business that produces and sells dairy products fromthe milk of the family cows, Daisy, Ermentrude, and Florence. Together, the three cowsproduce 22 gallons of milk each week, and Snape and his family turn the milk into icecream and butter that they then sell at the Farmers Market each Saturday morning.The butter-making process requires 2 gallons of milk to produce one kilogram of butter,and 3 gallons of milk is required to make one gallon of ice cream. Professor Snape owns

a huge refrigerator that can store practically unlimited amounts of butter, but his freezercan hold at most 6 gallons of ice cream.Snapes family has at most 6 hours per week in total to spend on manufacturing theirdelicious products. One hour of work is needed to produce either 4 gallons of ice creamor one kilogram of butter. Any fraction of one hour is needed to produce thecorresponding fraction of product.Professor Snapes products have a great reputation, and he always sells everything heproduces. He sets the prices to ensure a profit of $5 per gallon of ice cream and $4 per

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kilogram of butter. Y ou would like to figure out how much ice cream and butter heshould produce to maximize his profit.

4. Solve the following LPP by Two Phase or Big-M method.1 2

1 2

1 2

1 2

1 2

2

3 3

4 3 6

2 4

, 0

Maxz x x

Subjectedtox x

x x

x x

x x

5. Solve the following LPP by Dual Simplex method1 2

1 2

1 2

1 2

1 2

2

3 3

4 3 6

2 3

, 0

Maxz x x

Subjectedto

x x

x x

x x

x x

6. Solve the following LPP by Simplex method.1 2 3 4

1 2 4

1 2

2 3 4

1 2 3 4

2 4

3 4

2 3

3

, , , 0

Maximize Z x x x x

Subjectedto

x x x

x x

x x x

x x x x

7. Write the dual of the following Problem

1 2 3

1 2 3

1 2

2 3

1 2

3

3 4 5

2 3

2 4, 0

Minz x x x

Subjectedto

x x x

x x

x xx x

andx isunrestrictedinsign

8. Explain the importance of Sensitivity Analysis in LPP.9. Write the advantages of Two Phase method over Big M method.10.Write a short note on Dual Simplex Method.