# DOEACC Society 2006 DOEACC B Level B10 Applied Operations Research ( ) - Question Paper

Friday, 14 June 2013 03:45Web

Page 1 of 2

BE10-R3: APPLIED OPERATIONS RESEARCH

NOTE:

**Time:**three Hours Total

**Marks:**100

1.

**a)**In Operations Research

**(OR)**there are 2 distinct kinds of computations: those

involving simulation and those dealing with mathematical models. explain them briefly.

Why are calculations in OR mathematical models typically iterative?

**b)**A paper mill produce 2 grades of paper namely X and Y. Because of raw material

restrictions, it cannot produce more than 400 tons of grade X and 300 tons of grade Y in

a week. There are 160 production hours in a week. It requires 0.2 and 0.4 hours to

produce a ton of products X and Y respectively with corresponding profits of Rs. 200 and

Rs. 500 per ton. Formulate the above as a linear programming issue to maximize

profit.

**c)**Consider the subsequent problem:

minimize z = 3x1+4x2-5x3

subject to

2x1+3x2-5x3 ³ 10

x1-2x2-3x3 £ 8

x1,x2,x3 ³ 0

describe the dual issue.

**d)**What is Critical Path Method (CPM)? elaborate its main objectives?

**e)**Arrivals at a telephone both are considered to be subsequent Poisson process with an

avg. time of 10 minute ranging from 1 arrival and the next. Length of a phone call is

presumed to be distributed exponentially with mean three minutes.

**i)**What is the probability that a person arriving at the booth will have to wait?

**i**What is the avg. length of queue?

**i)****f)**Determine the optimal sequence of jobs, which minimizes the total elapsed time based

on the subsequent info.

Processing times on the machines A, B, C

Job A B C

1 three 3 5

2 eight four 8

3 seven two 10

4 five one 7

5 two five 6

g) The demand rate for an item in a company is 18000 units per year. The company can

produce at the rate of 3000 per month. The set-up-cost is Rs. 500 per order and the

holding cost is Rs. 0.15 per unit per month. Calculate:

**i)**optimum manufacturing volume

**i**maximum inventory.

**i)**(7x4)

BE10-R3 Page one of four July, 2006

**1.**ans ques. one and any 4 ques. from two to 7.

**2.**Parts of the identical ques. should be answered together and in the identical

sequence.

2.

**a)**The network in the subsequent figure represents the distances in miles ranging from different

cities i, i =1, 2, ….,

**8.**obtain the shortest routes ranging from the subsequent pairs of cities:

**i)**City one and city 8.

**i**City two and City 6.

**i)**4

2 one three 2

2

1 six 5

3 7

1 two 6

5 8

**b)**Determine the maximum flow ranging from nodes one and five for the network provided below:

(9+9)

**3.**Consider the integer linear programming problem:

maximize Z = 7x1+9x2

subject to

-x1+3x2 £ 6

7x1+x2 £ 35

x1, x2 nonnegative integers.

**a)**Using branch-and-bound algorithm (B&B), find the optimal solution.

**b)**Outline briefly the steps of B&B algorithm

Earning: Approval pending. |