# Pune University Previous Question Paper

## (2008 Pattern) (Sem. – II)

Time :3 Hours]                                                                                              [Max. Marks :100

Instructions to the candidates:

1)          All questions are compulsory.

2)          Assume suitable data, if necessary.

3)          Answers to the two sections should be written in separate books.

4)          Neat diagrams must be drawn wherever necessary.

5)          Pigures to the right indicate full marks.

6)          Use of logarithmic tables slide rule, Mollier charts, electronic pocket calculator and steam tables is allowed.

SECTION – I

QI) Explain the classification of Production Systems in detail with suitable examples.                                                                                                                                                               [16]

OR

Explain the functions of Production Planning and Control in detail with suitable examples.                                                                                                                                 [16]

Q2) Consider a project consisting of 12 activities with following precedence relationship and durations.                                                                                                             [16]

 Activity A B C D E F G H I J K L Immediate predecessor – – A a A D C D E,F B,I G,H J,K Duration (weeks) 4 8 2 4 9 1 7 3 2 2 5 4

a)             Draw network diagram 8 find the critical path.

b)            List the total float, free float and independent float for all activities.

OR

The time estimates (in weeks) for the activities of a PERT network are given below.

 Activity T 0 T m T p 1-2 1 1 7 1-3 1 4 7 1-4 2 2 8 2-5 1 1 1 3-5 2 5 14 4-6 2 5 8 5-6 3 6 15

i)                 Draw the project network and determine expected project length.

ii)                Calculate the Std. Dev. And variance of the project.

iii)               What is the probability that project will be completed no more than

4                 weeks earlier than expected time.

iv)               If the project due date is 19 weeks, what is the probability of not meeting the due date.                                                                                                      [16] Given data : Z = 1.33, P = 0.9082

Z = 0.67, P = 0.7486 Z = 1.28, P = 0.9

Q3) There are seven jobs, each of which has to go through the machines A 8 B in the order AB. Processing time in hours are given as,

 Job 1 2 3 4 5 6 7 Machine A 3 12 15 6 10 11 9 Machine B 8 10 10 6 12 1 3

 Determine the sequence of these jobs that will minimize the total elapsed time T. Also find T and idle time for machines A and B.                                                                                                                                                                                                       [18]

OR

There are five jobs, each of which is to be processed through three machines A, B and C in the order ABC. Processing times in hours are,

 Job 1 2 3 4 5 Machine A 3 8 7 5 4 Machine B 4 5 1 2 3 Machine C 7 9 5 6 10

Determine the optimum sequence for the five jobs and the minimum elapsed time. Also find the idle time for the three machines and waiting time for the jobs.                              [18]

SECTION – II

Q4A A j ob production unit has four j obs A, B, C and D, which can be manufactured on each of the four machines. The processing cost of each job for each machine is given. How should the jobs be assigned so as to minimize the processing cost.                                                                                                                                                                                                                                                [16]

P Q R S

 A 31 25 33 25 B 25 24 23 21 C 19 21 23 24 D 38 36 34 40

OR

Solve the following Assignment problem for minimization. The costs are given below. Find all the alternate solutions, if any.                                                                              [16]

 X1 X2 X3 X4 X5 A 15 29 35 20 38 B 21 27 33 17 36 C 17 25 37 15 42 D 14 31 39 21 40 E 19 30 40 19 18

Q5) Find the initial feasible solution for the following problem. The supply, demand

and unit cost figures are given.

W1 W2 W3 W4

 P1 190 300 500 100 70 P2 700 300 400 600 90 P3 400 100 400 200 180 50 80 70 140

 Demand ^

OR

 S1 10 20 5 7 S2 13 9 12 8 S3 4 15 7 9 S4 14 7 1 0 S5 3 12 5 19
 Solve the following Transportation problem. D1 D2 D3 D4

Q6) A company makes three products X, Y and Z which go through three departments – Drill, Lathe and Assembly. The hours of department time required by each of the products, the hours available in each of the departments and the profit contribution of each of the products are given in the following table.

 Products Time required per unit (Hours) Profit Contribution (Rs. per Unit) Drill Lathe Assembly X 3 3 8 9 Y 6 5 10 15 Z 7 4 12 20 Hrs. Available 210 240 260

The marketing department of the company indicates that the sales potential for the products X and Y is unlimited, but for Z it is not more than 30 units. Determine optimum production schedule.                        [18]

OR

A company machines and drills two castings X and Y. The time required to machine and drill one casting including machine set up time is as follows.

 Casting Machine Hours Drilling Hours X 4 2 Y 2 5

There are two lathe and three drilling machines. The working week is of 40 hours; there is no overtime and lost time. Variable costs for both the castings are Rs. 120 per unit while the total fixed costs amount to Rs. 1000 per week. The selling price of casting X is Rs. 300 per unit and that of Y is Rs. 360 per unit. There are no limitations on the number of X and Y castings that can be sold. The company wishes to maximize profits. Formulate the linear programming model for the same.                                                                                                                                                                                                             [18]