Operations Research Test

Operations Research Test

At a ticket booking centre, if the mean arrival rate of customers is 10 per hour and the mean service rate is 20 per hour, calculate the traffic intensity.

a. 30 per hour

b. 10 per hour

c. 2 per hour

d. 0.5 per hour

A petrol pump is opening a customer service centre which will be having only one counter to attend to the people. The manager estimates that the customers will arrive at the rate of 25 per hour. The customer care executive who has been considered for the post can attend customers at the rate of 1 customer every 2 minutes. Assuming Poisson arrivals and exponential service, calculate the average waiting time of the customers.

a. 1/5^th of an hour

b. 1/8^th of an hour

c. 1/3^rd of an hour

d. 1/6^th of an hour

In Goal Programming, which of the following is not an application of optimization?

a. Component Selection

b. Dynamic load sharing

c. Calculus of variations

d. Load allocation problems

The graphical method for solving transportation problems can be applied to __________ variables.

a. 5

b. 2

c. 3

d. 4

A furniture shop has employed only one carpenter whose work varies according to the number of wooden frames he makes. The working rate of the carpenter is randomly distributed approximating a Poisson distribution with a mean rate of ten wooden frames per hour. The carpenter works for 10 hours a day and gets an order of making 5 wooden frames per hour. If the hack-saw used by the carpenter is valued at $20 per hour, determine the equipment utilization.

a. 0.1

b. 0.3

c. 0.5

d. 0.7

In which of the following fields is Linear Programming technology not useful?

a. Crude oil distribution to refineries

b. Production distribution

c. Agricultural operations

d. Military applications

e. Inventory problems

From the above table, find the basic feasible solution using the matrix minimum method.

a. 6260

b. 7260

c. 8260

d. 9260

The increase in the probability of a failure with the increase in the life of an item is termed ___________.

a. gradual failure

b. progressive failure

c. retrogressive failure

d. random failure

From the above table, determine which alternative is the best to choose if a person is adopting the Laplace criterion.

a. Stock pile X and associated cost $80000

b. Do not stock pile Y and associated cost $70000

c. Stock pile X and associated cost $40000

d. Do not stock pile Y and associated cost 0

From the above table, determine which alternative is the best to choose if a person is adopting the Savage criterion.

a. Stock pile X and associated cost 0

b. Do not stock pile Y and associated cost $30000

c. Stock pile X and associated cost $10000

d. Do not stock pile Y and associated cost 0

Solve the game the pay off matrix of which is given by:

  

a. -3 and +3

b. -2 and +2

c. -4 and +4

d. -5 and +5

In the above table, the mortality rates for a certain type of health products have been given. Calculate the probability of failure at the end of the 3^rd month.

a. 0.15

b. 0.25

c. 0.35

d. 0.45

Which among the following is not an application of Goal Programming?

a. Capital project evaluation

b. Establishing sales targets

c. Analyzing a multiplant scheduling process

d. Improving the work conditions having highly fluctuating demands

According to the Poisson distribution process analysis, patients come to a hospital at a mean rate of 50 per hour. The time required to attend a patient has an exponential distribution with a mean of 100 per hour. Assuming that every patient is attended by an individual doctor, what would be the waiting time of one patient?

a. 20 minutes

b. 25 minutes

c. 30 minutes

d. 35 minutes

The simulation technique must be used __________.

a. when the system's actual observation is expensive

b. when the problem to handle is very small

c. when the standard sensitivity analysis is easy to handle

d. when it is easy to develop a mathematical model

Which among the following methods is known as the Unit Penalty Method?

a. North west corner rule method

b. Matrix minimum method

c. Vogel approximation method

d. Stepping stone method

Use the property of dominance to find out the value of the saddle point.

a. 25/7

b. 30/7

c. 7/25

d. 7/30

Which among the following is not an element of the Project Schedule Characteristic of PERT/CPM?

a. Developing a network diagram

b. Re-allocation of resources

c. Estimating the duration of activities

d. Resource availability

Which among the following characteristics of the game theory involves the quantitative measure of satisfaction?

a. Chance of strategy

b. Pay-offs

c. Alternatives

d. Chance of activities

A manufacturing unit makes 40 units of an automobile part daily. Study the above table and calculate how many more pieces need to be produced to meet the customer demand for the coming 5 days.

 

The demand value is according to random numbers.

a. 35

b. 45

c. 50

d. 55

The Simplex method can solve____________

a. equations which have equal numbers of unknowns.

b. equations which have less numbers of unknowns than the equation itself.

c. equations which have more numbers of unknowns that the equation itself.

The Vogel's approximate method in Linear Programming is used in solving __________ problems.

a. graphical

b. transportation

c. marketing

d. waiting time

From the above table, determine the best alternative to choose if a person is adopting the maximax criterion.

a. Alternative X

b. Alternative Y

c. Alternative Z

__________is not an element of Sensitivity Analysis.

a. Range

b. Forecasting

c. Profitability

d. Insolvency

Which among the following is a characteristic of Dynamic Programming?

a. Dynamic programming is a strong computational technique.

b. Dynamic Programming is too analogous to solve a group of consecutive linear equations.

c. Dynamic programming does not permit determining of optimal decisions.

d. Dynamic Programming is a multistage decision making process.

 

From the above table, determine the best alternative to choose if a person is adopting the optimistic criterion.

a. Stock pile X and associated cost $30000

b. Do not stock pile Y and associated cost $90000

c. Stock pile X and associated cost $60000

The Monte-Carlo simulation technique ___________.

a. uses random numbers for generating data

b. is used to solve stochastic situations

c. uses mathematical techniques to solve all problems

d. is used where physical experimentation with the actual system is possible

A company makes two products A and B. The profit per unit of the two products is $80 and $100 respectively. Both the products are sold in three cities. The above table indicates total products sold per week in the three cities.

Formulate this product problem in the Linear Programming Form.

a. 3x1 + 2x2 ≤ 250
    4x1 + 3x2 ≤ 300
    5x1 + 2x2 ≤ 500

b. 3x1 + 2x2 ≥ 250
    4x1 + 3x2 ≥ 300
    5x1 + 2x2 ≥ 500

c. 3x1 + 2x2 = 250
    4x1 + 3x2 = 300
    5x1 + 2x2 = 500

Study the above table and calculate the project's normal distribution(in terms of days).

Calculate the cost of the project if the indirect cost is $100 per day.

a. $1220

b. $1320

c. $1120

d. $122000

In the above table, 6 jobs are given along with their operation time in minutes. Find out the average processing time.

a. 20 minutes

b. 22 minutes

c. 24 minutes

d. 26 minutes

Find the value of the above game using the principle of dominance.

a. -5

b. 8

c. 7

d. 3

e. No saddle point

Which one of the following is a cycling error in the Network Logic of PERT/CPM?

a. Looping error

b. Dangling error

c. Merging error

d. Bursting error

Which of the following types of cost is dependent upon the amount of utilization of resources during the execution of individual activities?

a. Project cost

b. Indirect cost

c. Direct cost

At an interview, the candidates arrive according to the Poisson distribution process with an average time of 10 minutes between each candidate's arrival. The interviewing line is exponentially distributed with a mean time of 5 minutes. On the basis of this information, calculate the average queue length.

a. 1/5

b. 1/4

c. 1/3

d. 1/6

A person comes to a cyber cafe everyday. Sometimes, he has to wait for the cyber cafe to open and at other times, he arrives late. The opening time of the cafe varies from day to day. Study the above table, computed for 8 days, and calculate the average waiting time of that person. 

a. 2.2 minutes

b. 3.2 minutes

c. 4.2 minutes

d. 5.2 minutes

A bus arrives at a bus-stand every 10 minutes and the service time is 30 minutes. If the capacity of the bus-stand is 5 buses, calculate the probability of the bus-stand being empty.

a. 0.0027

b. 0.002

c. 0.0057

d. 0.0037

A discotheque has a single ticket-counter. During rush hours, people arrive at the rate of 50 per hour. The average number of people allowed to enter is 100 per hour. Calculate the average number of people who still have to wait in the queue for their turn.

a. 2

b. 3

c. 4

d. 1

Develop a network diagram based on the information given in the table. 

a. A

b. B

c. C

d. D

Which among the following is not an application of optimization in linear programming?

a. Component selection

b. Dynamic load sharing

c. Calculus of variations

d. Load allocation problems

 

Study the above table and calculate the range of the random numbers in which the sum of the average value of the demand and the average value of the profit falls.

a. 30-50

b. 40-80

c. 80-55

d. 55-65