Gujarat University 2009-8th Sem B.E Mechanical Engineering Operation Research-II, , , Gujrat University - Question Paper

B.E. Sem. VIII (Mech.)

June-2009 Operations Research

Attempt all questions.

Figures to the right indicate the full marks. Assume additional data if necessary.

Use graph paper for graphical solution.

1. A garment manufacturing company has 4 manufacturing units and 4 sales locations. The cost of production per unit garment at manufacturing unit is as under:    18

Manufacturing Unit    A    B    C    D

Cost (Rs.)    100 150 1 200    250

The sales price per unit garment at sales location is as under.

Sales location    P    Q    R    S

Sales Price (Rs.)    300 350 325    350

The other cost and the transportation cost per unit garment from manufacturing unit to sales location is as shown in the following matrix.

Sales Location P Q R S A 25 25 50 75 Manufacturing Unit B 50 25 75 25

C 25 50 25 50 D 75 75 50 25

The data related to production capacity of the manufacturing units and demand of sales locations is as under.

Production capacity	A	B	C	D
(Units)	25	50	50	25
Demand	P	Q	R	S
(Units)	50	25	50	25

Formulate the problem as transportation problem and decide the distribution plan for the company so as to make optimal profit at the sales location.

2. (a) What is degeneracy in simplex method ? How can it be resolved ?    18

(b) A chemical compound requires minimum 80, 60 and maximum 90 units of ingredients A, B and C respectively. Three types of chemicals are available in market containing these ingredients as under.

Ingredient Content (Units/Unit of chemical)

Chemical	A	B	C	Cost (Rs./Unit)
1	1	2	1	300
2	3	2	1	300
3	1	1	2	500

Formulate the problem as linear programming problem and solve it.

3. (a) Use Big-M method to solve the following:    16

Minimize Z = 3x_} + 8x₂

S.t.    x_l+x₂ = 200

jCj + 0x₂ < 80 Oix₁ + Jtj > 60 Xj & Xj > 0

(b) Graph the following inequalities and show the solution space:

-Xy + 2x₁ > 100

-3x, + 4x₂ <, 300 4xj + 6x2 < 600 jtj & > 0

OR

(a)    Use two phase method to solve the following:

Maximize Z = 5x, + 10x₂

S.t.    2x, +jc₂6

Xj + 2x₂ - 6 x, + x₂ > 4 x, & x₂10

(b)    Construct the dual of the following primal problem and solve it.

Maximum Z = 3xj + 2x₂

S.t.    2xj+x2<5

x,+x₂<3 Xj & x₂ > 0

There are six subjects to teach the students and five professors are available. Each professor is capable to teach any one of the six different subjects. The class preparation time in hours for different subjects varies from professor to professor and is given in the following matrix.    16

Professor

S, s2 Subject S3 S4 s5 s6 pl 12 10 15 22 18 8 *2 10 18 25 15 16 12 P3 11 10 3 8 5 9 6 14 10 13 13 12 P5 8 12 11 7 13 10

Using assignment technique determine which subject should be given to the visiting professor, if each professor can be assigned only one subject and visiting professor can be called for any subject.

OR

A manufacturing company has four machines and has to produce four parts, one part on each machine. The cost of producing each part on different machine is as shown in the following matrix.

Part	Machine Mi m3 m4 p. 12 9 11 13 P2 8 8 9 6 P3 14 16 21 13 P4 14 15 17 12

The company plans to add a new machine in the present facility by replacing one of the present machines. The cost to produce each part on the new machine is as shown below.

Part    Pi 2 P3 4

Cost (Rs.) 11-7 15 10 Using assignment technique determine:

(i)    Should the company add the new machine ?

(ii)    It yes, which machine should be replaced ?

(a)    Discuss the reasons for replacement of an equipment.    16

(b)    The maintenance and resale value per year of a machine whose purchase price is Rs. 7,000 is given below :

Year    1 2 3 4 5 6 7 8

Maintenance Cost (Rs.) 900 1,200 1,600 2,100 2,800 3,700 4,700 5,900 Resale Value (Rs.) 4,000 2,000 1,200 600 500 400 400 400

Find out when should the machine be replaced ?

OR

(a)    Discuss the replacement policy for items whose running cost increases with time but value of money changes with constant rate during the period.

(b)    A firm has purchased an equipment in Rs. 10,000. The operating and maintenance costs are about Rs. 2,500 per year for the first two years and then go up by approximately Rs. 1,500 per year. When the equipment should be replaced if the discount rate is 10% per year ?

Describe the basic queuing process.

Name the various elements of queuing system.

The machines in production shop breakdown at an average of 2 per hour. The nonproductive time of any machine costs Rs. 30 per hour. If the cost of repairman is Rs. 50 per hour and the repair rate is 3 per hour. Calculate

(i)    Number of machines not working at any point of time.

(ii)    Average time that a machine is waiting for the repairman.

(iii)    Cost of non-productive time of the machine operator.

(iv)    Expected cost of system per hour.

OR

Give the classification of Games.

Describe the terminology used in two persons zero sum games.

Calculate the value of game if the payoff matrix for a particular competitive situation is as under

B

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Attachment: gujarat-university-2009-b-e-mechanical-engineering-33394-1.pdf

Earning:   Approval pending.