End Semester Examinations –  march/April 2015

The minimum working capacity of each department is 100, 75, and 80 hours respectively. The Profit on the sale of one kg of cheese, butter and milk candy is Rs.12, Rs.10 and Rs.8 respectively. You have to plan to schedule that maximizes the total profit. Bring out a mathematical model

            Maximize Z=5x+10y

               Subject to 2x+y≥8

                               3x+4y≤24

                                       y≥2

                                    x,y≥0

1. What is the average length of the waiting line to be expected under the existing conditions?
2. What portion of his time is the cashier expected to be idle?
3. What is the average length of time that a customer would be expected to wait to pay for his purchase?
4. If it was decided that a customer would not tolerate a wait of more than 12 minutes, what is the probability that a customer would have to wait at least that length of time?

a)      Optimal job assignment                         b) The cost of assignmetns.

Machinist                             Job

                        1        2          3         4        5

A                 10       3          3         2        8

   B                   9        7          8         2        7

   C                  7         5          6         2        4

   D                  3         5          8        2        4

   E                   9       10         9         6       10

8.

It is known that currently nothing can be sent from warehouse 1 to market A and from warehouse 3 to market C. Find the initial solution to the problem using Vogel’s Approximation Method.

9.

Obtain the dual of the following

Maximize Z=8X1+10X2+5X3

Subject to constraints

X1-X3≤4

   2X1+4X2≤12

   X1+X2+X3≥2

   3X1+2X2-X3=8

   X1,X2,X3≥0

10.

You are given the information about the cost of performing different jobs by different persons. The job-person marking x indicate that the individual involved cannot perform the particular job,. Using this information state

i)                   The optimal assignment of jobs (ii) the cost of such assignment

SECTION – B

Cabinets which requires the following task.

The wheels are mounted after they are prepared. The base cannot be attached until the sides are assembled and wheels mounted. The  top cannot be attached nor the brackets inserted until the sides are assembled. The shelves are inserted after the brackets are installed. The back panel is attached after the base and top are attached. The doors are attached after the selves are inserted and the top and bases are attached. The unit is painted after the back and the doors Are attached.

1. Identify the immediate predecessors of each task and draw the network.
2. Find the critical path(s) and list the critical activities.
3. Obtain the earliest and the latest start and the completion times of all the a ctivities and their total floats, free float and independent floats.

12.

Find x1 and x2 so as to maximize Z=24×1 +18×2

Subject to constraints 4×1 +6×2≤24

6×1  + 3×2≤18

With                                x1,x2≥0

13.

Maximize  Z=2X1+4X2-X3

Subject to constraints

X1+X2+X3≥8

X1-X2≥1

3X1+4X2+X3≤40

Where X1, X2, X3≥0

14.

a) In a game of matching coins with two players suppose A wins one unit of value when there are two heads, wins nothing when there are two tails, and loses ½ unit of value when there are one head and one tail. Determine the payoff matrix A, the best strategies for each player and the value of the game to A.

b) The optimistic, most likely and pessimistic times of the activities of a project are given below. Activity 40-50 must not start before 22 days while activity   70-90 must end by 35 days. The scheduled completion time of the project is 46 days. Draw the network and determine the critical path. What is the probability of completing the project in scheduled time?

SECTION – C

Using Simulation process repeat the trial 10 times, compute the values for demand, profit and investment. What is the most likely return percent on investment?

Random numbers : (30, 12, 16)  (59, 09, 69) (63,94,26) (27, 08, 74) (64, 60, 61) (28, 28, 72)  (31, 23, 57) (54,85,20) (64, 68, 18)  (32, 31, 87)

In the bracket above use the first number for demand, second for profit and last for investment required.

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