Operations Research — Winter 2018

Define the following terms:

Operations Research (ii) Objective Function (iii) Events (iv) EOQ

Idle Time on a Machine (vi) Failure (vii) Optimal solution

Use graphical method to solve the following LP problem. Maximize Z=15x + 10x12 Subject to constraints

4x + 6x ≤ (ii) 3x + 0x ≤ 18012 (iii) 0x + 5x ≤ 20012 And x1 , x2 ≥ 0

Solve the following LP problem using Simplex Method. Max z = 3x + 2x + 5x123 Subject to the constraints

x + 2x + x ≤ (ii) 3x + 2x ≤ 46013 (iii) x + 4x ≤ 42012 And x1 , x2 , x3 ≥ 0

Acompany makes two products (say, Pand Q) using two machines (say, A and B). Each unit of Pthat is produced requires 50 minutes processing time on machine Aand 30 minutes processing time on machine B. Each unit of Qthat is produced requires 24 minutes processing time on machine Aand 33 minutes processing time on machine B. Machine Ais going to be available for 40 hours and machine Bis available for 35 hours. The profit per unit of Pis $25 and the profit per unit of Qis $30. Formulate this problem as an LP model to determine the production quantity of each product in such a way as to maximize the total profit, given that the available resources should not be exceeded.

Construct the dual of the problem Min = 3x - 2x + 4x z 1 2 Subject to 3x + 5x + 4x ≥ 7,123 6x + x + 3x ≥ 4,123 7x - 2x - x ≤ 10,123 x - 2x + 5x ≥ 3,123 4x1 + 7x2 - 2x3 ≥ 2, And x ,x x ≥ 0. 1 2,

Explain the various steps involved in solving transportation problem using

North West Corner Method (ii) Least Cost Method.

Find the initial basic feasible solution of the following transportation problem:

NWCM (ii) LCM Plants Ware houses D1 D2 D3 D4 Supply S1 19 30 50 10 S2 70 30 40 60 9 S3 40 8 70 20 18 Demand 5 8 7

Abook binder has one printing press, one binding machine and manuscripts of a number of books. The time required for performing the printing and binding operations on each book are shown below. The binder wishes to determine the order in which the book should be processed, so that the total time required to process all books is minimized. Book 1 2 3 4 5 Printing time (Hours) 30 120 50 20 90 110 Binding time (Hours) 80 100 90 60 30

What is Simulation? Explain the advantages and disadvantages of Simulation.

i) Define the terms: (I) Saddle Point (II) Value of the Game (III) Fair Game ii) Find the range of values of p and q which will render the entry(2,2) a saddle point for the game Player B245 10 7 q 4 p

Explain the structure of the Queuing System.

An Accounts Officer has 4 subordinates and 4 tasks. The subordinates differ in efficiency. The tasks also differ in their intrinsic difficulty. His estimates of the time each would take to perform each task are given in the matrix below. How should the tasks be allocated one to one man, so that the total man hours are minimized? Task I II III IV subordinate 2 13 28 4 26

What is Replacement? Explain the types of failures with example.

Asmall assembly plant assembles PCs through 9 interlink stages according to the following precedence / process. Stages From 1 1 1 2 2 3 4 5 6 6 7 To 2 3 4 4 5 6 6 7 7 8 8 92 Hours 4 12 10 8 6 8 10 10 0 8 10

Draw an Arrow Diagram (Network) representing the above assembly work. (ii) Tabulate Earliest Start, Earliest Finish, Latest Start and Latest Finish time for all the stages. (iii) Find the Critical Path and the Assembly Duration. (iv) Tabulate the Total Float, Free Float and Independent Float.

Explain the difference between PERT and CPM.

The production department of a company requires 3,600 kg of raw material for manufacturing a particular item per year. It has been estimated that the cost of placing an order is Rs. 36 and the cost of carrying inventory is 25% of the inventories. The price is Rs. 10 per kg. Help the purchase manager to determine an ordering policy for raw material.