3. Which of the following is a valid objective function for a linear programming problem?

a. Max 5xy b. Min (x1 + x2)/x3 c. Max 5x2 + 6y2 d. Min Z = 4x + 3y

4. Which one of the following is not an example of Queue? a. cars waiting at petrol pump b. customers waiting at bank c. arrangement of colours in a row d.

machines waiting for repair

5. How many basic and non-basic variables are defined by the following the linear equation?

2X1 + 3X2 - 4X3 + 5X4 = 10

a. one variable is basic, three variables are non-basic b. two variables are basic, two variables are

non-basic c. three variables are basic, one variable is non-basic d. all four variables are basic

Group BShort answer type questions 5x2=10

Attempt as per the instructions given below6. Solve the following linear programming problem using graphical approach.

Minimize Z = 200X1 + 300X2

Subject to, 2X1 + 3X2 ≥ 1200X1 + X2 ≤ 4002X1 + 1.5X2 ≥ 900X1, X2 ≥ 0

OR

Find out the dual form of the following primal problem. 9

Min Z = 5 X1 + 7X2 + 9 X3

Subjected to

X1+X2+X3 = 20

X1+3X2+5X3 ≥ 60

5X2 - X3 ≤ 10

X3 ≥ 4

X1, X2, X3 ≥ 0

7. Three jobs A, B and C are to be assigned to three machines X, Y Z. The processing costs are as given in the

matrix shown below. Find the allocation which will minimize the overall processing cost. Use Hungarian approach.

Machines

Jobs X Y Z

A 19 28 31

B 11 17 16

C 12 15 13

OR

There are 3 plants which supply the following quantity of coal P 1= 50 kg, P2=40 kg, P3= 60 kg. There are 3

consumers who require the coal as follows C1= 20 kg, C2= 95 kg, C3= 35 kg. The cost matrix in Rs. / kg is given in

the matrix. Find the schedule of transportation policy using north-west corner rule which minimizes the total

transportation cost. Also check for degeneracy.

6 4 13 8 74 4 2

Group C

Long answer type questions 15x1=15

8. a) Explain the basic elements of the 1st model of Queuing theory. Also write the significance of all its elements.

b) A TV repairman finds that the time spent on his jobs has an exponential distribution with a mean of 30 minutes. If

he repairs sets in the order in which the come in, and if the arrival of the sets follows a Poisson distribution with an

average rate of 10 sets per 8 hours day, what is the expected idle of the repairman per day. How many sets are ahead

of the average sets just brought in? 6+9