Sub Name : Operation Research and Optimization Techniques

CS/ B.Tech (CSE) / SEM-4ENGINEERING & MANAGEMENT EXAMINATION, DECEMBER- 2008Operation Research and Optimization Techniques

SEMESTER-4__________________________________________________________________GROUP A

(Multiple choice type questions ) 10 X 1 = 10

1. Answer questions from the followings.

Transportation problem can be maximization or can be a minimization problem.

a. TRUE b. FALSE c. cant be determined d. It can only be a minimization problem.xx

The maximization problem in the Primal becomes ________________________ problem in its dual. A. 2X2 Game B. Minimizationxx C. zero sum game D. none of these

In which method Artifical variable is used.? Simplex method b. Big M method c. two phase methodxx d. none.

The point of intersection of a pure strategy game is called ________________________.

a. Value of the gamexx b. two person game c. mixed strategy game d. none

The possible number of basic solutions in a system of m equations in n unknowns is ____________.

a. m Cn b. n >= m xx c. nPm d. mPnPlayer BB1B2B3

A1152 3

A2657

A3746

The optimum strategy for A and B will be __________.

a. A1 and B3b. A1 and B1 c. A1 and B2 Player A d. A2 and B2xx

The time estimates for a particular activity be : T0 = 5 days ; Tm = 7 days; Tp = 9 days. Then expected time Te is ______________________________.

A. 10 days. B. 15 Days xx C. 5 days. D. 7 days.

In assignment problem which method is used ?

A. NW corner method B. VAM xx C. Hungarian method D. None

Expected waiting time a customer spends in the queuing systems is Ws = ______________.

A. 1 / B. C. D.

Test for optimality in simplex method (in case of maximization problem ) is ______________

A. Zj Cj >= 0 xx B. Z >= 0 C. Cj Zj >= 0. D. Zj = 0In queuing model utilization factor is ____________________.

A.B.C.D.

The more efficient method for transportation problem is _____________________.

A. MODI B. NW corner method C. VAM xxD. Simplex

In a mixed strategy game (2 X n GAME ) which method should be applied first .

A. Simplex method B. Graphical method solution xxx C. saddle point solution D. VAM

Solve the transportation problem .

W1 W2 W3 W4 Capacity F1 10 30 5010 7

F2 70304060 9

F3 40 8707018

Requirements: 5 8 7 14 34

3. Solve the following optimization problem Graphically.

Maximize Z = 5x1 + 4x2

Constraints :: 6x1 + 4x2 < = 24X1 +2x2 = 0 and x3 is unrestricted .

GROUP C (Long answer Type question ) (Answer questions from the following)5 Find the dual of the following problem .

Max (Zx) = 2X1 + 3X2 - 4X3

S.t :: 3X1 + X2 + x3 = 4. X1 5X2 + x3 = 5. where x1 , x2 , x3 >= 0

15X &X company produces branded shirts.. It has 3 factories in 3 different locations where shirts are produced. Each factory has its own capacity to produce some number of shirts per week. X&X co. has its 3 departmental stores where these shirts are sold. The requirement/demand per week for these shirts at each store is given below. The cost of transport is also given for each combination of factory & Departmental store. Find out the minimum cost required to fulfill the demand for three stores per week.

Apply a method to Check whether the optimal solution is achieved on not. Is the optimal solution degenerate? TO

FROM Store 1

Store 2 Store 3Factory Capacity --

Factory 1 543100

Factory 2 843300

Factory 3 975300

Demand for stores ----300200200

7.A ) A departmental store has a single cashier. During rush hours , customer arrive at the rate of 20 customers / hour . The average number of customers that can be processed by the cashier is 24/hour. Assume it is a single channel queuing model and answer the questions. 10

Probability that the cashier is idle.

Average no. of customers in the queuing system.

Average time the customer spends in the system.

The probability that there are at least two customers in the system.

The probability that no customer is in the queue.

7. B) Find the optimal assignment for the following problem. Which employee is best suited for which job? 5

Employee 1Employee 2Employee 3Employee 4

JOB 1352728

37

JOB 22834

2940

JOB 3

35243233

JOB 4

24322528

8 A) For the Network given below , the activity time in days are given along the arrows. Calculate the slacks for the events and determine the critical path . 10

8. B ) Write down the Rule of Dominance with a small example. 5

89. A) A Company produces two products X AND Y. The sales volume for X is at least 40% of the total sales of both X and Y. The market survey ensures that it is not possible to sell more than 10 units of X per day. Both product need one raw material and supply of raw material is upto 12 kg per day.The usage rates of the raw material are 1 kg per unit for product X and 2kg per unit of product Y. the unit sale prices for X and Y are Rs. 200 and Rs. 300 respectively. Formulate the LPP and solve it graphically.

9. B) Solve the game using graphical method and show the graph with proper explanation.7

B1 B2 B3 B4

1302

301-1

A1

A2