GATE PI Operation Research PYQs & Answers — Page 2

Questions 11–20 of 21. Imported answers require independent review unless marked reviewed.

If the interarrival time is exponential and 8 customers per hour arrive in a bank, then the probability of no arrival of customer during a period of 15 minutes is____________. [round off to two decimal places]

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

A vaccine has to be distributed from two warehouses to three hospitals. The supplies at warehouses W₁ and W₂ are 200 and 150, respectively. The demands at hospitals H₁, H₂, and H₃ are 100, 150 and 125, respectively. The transportation cost (in ₹) per vaccine is as follows:

| | H₁ | H₂ | H₃ | | W₁ | 5 | 7 | 3 | | W₂ | 4 | 6 | 7 |

The initial basic feasible solution using the Northwest-corner method provides the total transportation cost (in ₹) as____________. [round off to nearest integer]

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Consider the linear programming problem:

Maximize

subject to

(C₁)

(C₂)

(C₃)

The optimal solution is given as

and

. The dual variables of constraints C₁, C₂ and C₃ are

and

, respectively. The optimal values of dual variables are

and

. The value of parameter P in the objective function is____________. [round off to one decimal place]

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

A company manufactures two products P and Q with unit profit of 4 and 5, respectively. The production requires manpower and two kinds of raw materials R1 and R2. The following table summarizes the requirement and availability of resources.

Resource	Resource usage per unit of production P	Q	Amount of resource available
manpower	1	1	10
R1	1	2	18
R2	2	1	18

The maximum profit the company can make is

Your answerChoose one option.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

The Bellman’s principle of optimality is related to

Your answerChoose one option.

Linear programming problem

Transportation problem

Dynamic programming problem

Assignment problem

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

A company manufactures products P and Q in quantities

and

, respectively, using two resources. The following Linear Programming Problem (LPP) is formulated to maximize the profit Z.

Maximize

subject to

(for Resource 1)

(for Resource 2) and

The shadow price for Resource 2 is

Your answerChoose one option.

2/3

4/3

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

A warehouse has 1 loading dock and 3 persons for loading operations. The arrival rate of trucks follows Poisson distribution with a mean of 4 trucks/hour. The average loading time (by three persons together) per truck is exponentially distributed with a mean of 10 minutes. The charge of the trucks per hour and loading charges per person per hour are Rs.20 and Rs.6, respectively. The total cost (in Rs./hour) is _____

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

An LPP is defined as Minimize

subject to,

The objective function of the dual of this LPP is

Your answerChoose one option.

Maximize

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

In a service centre, cars arrive according to Poisson distribution with a mean of 2 cars per hour. The time for serving a car is exponential with a mean of 15 minutes. The expected waiting time (in minute) in the queue is

Your answerChoose one option.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

A company has two manufacturing plants (C

and C

) and two distribution centres (D

and D

). The capacities of C

and C

are 100 and 200 units, respectively. The demand for D

and D

are 190 and 110 units, respectively. The costs per unit (in Rs.) of transportation at different routes are as per the following matrix: | | D

| D

| C

| 22 | 21 | C

| 20 | 27 | The minimum total cost (in Rs.) of transportation is _____

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

GATE PI Operation Research PYQs

Question 33

Question 62

Question 63

Question 32

Question 21

Question 33

Question 25

Question 33

Question 31

Question 44