Ques 1.

The optimal solution of any integer linear programming problem can be obtained by rounding off the optimal solution of its LP relaxation.

Ques 2.

In an optimal solution  of the LPP

s.t.

  both cannot be positive.

Ques 3.

An assignment problem can be considered as a special case of transportation problem.

Ques 4.

In the inventory model with finite replenishment rate, if the replenishment rate is equal to consumption rate, the holding cost is 0.

Ques 5.

For a Queuing Model (M/M/1): (GD/∞/∞) with one server, if the service rate µ increases, the expected number of customers in the system decreases.

Ques 6.

A sugar manufacture has two production processes. In one hour, Process I makes 100 kg of Grade I (high quality) sugar and also produces 140 kg of Grade II sugar as a byproduct. Process II makes in one hour 60 kg of Grade I (high quality) sugar and also produces as a by-product 40 kg of Grade II sugar. The manufacture is confident that during the festival season all the sugar that is made can be sold. He has committed to selling at least 6000 kg of Grade I and 5600 kg of Grade II for the season. The revenue earned by selling one kilogram of Grade I sugar is ₹ 4 (irrespective of the process used) and the revenue earned by selling one kilogram of Grade II sugar is ₹ 2 (irrespective of the process used). Formulate the problem of maximizing the total revenue earned as an LPP. Solve the problem by graphical-method.

Ques 7.

Customers come to a coffee shop at the average rate of 32 per day (8 hours a day) in Poisson pattern. The waiter employed to serve the customers has left the job. The owner of the shop wants to hire a new the job. The owner of the shop wants to hire a new waiter. Two applicants, Abdul and Raju, have applied for the post. The service times of Abdul and Raju are exponentially distributed with mean 12 minutes and 10 minutes, respectively. Abdul and Raju demand salaries of ₹ 135 and ₹ 165 per day, respectively. If no service is available, the average loss to the owner is ₹ 400 per day. Who among the two should be selected for the job?

Ques 8.

A manager wants to the appoint 4 sales-persons to 4 different cities. If the expected profit when different persons are appointed to different cities is a given in the table below, find the assignment that will maximize the profit:

Ques 9.

An oil engine manufacture purchase lubricants at the rate of  50 per unit from a vendor. The requirement of these lubricants is 1800 units per year. The cost of placing an order is  40 and inventory carrying cost per rupee per year is only 20 paise. Find the Economic Order Quantity (EOQ). Also find the cycle time.

Ques 10.

) The following is the optimal table of a maximising LPP where   are slack variables.

Suppose a new constant 8 2x1 + x2 ≤ is added to the LPP. Find the new optimal solution of the resulting LPP.

Ques 11.

In a factory there are 6 jobs to be processed on two Machines A and B. The processing times are given in the table below. The jobs are first processed on Machine A and then on Machine B. Find the optimal job sequence and the minimum elapsed time.

Job:
Machine A:	1	3	8	5	6	3
Machine B:	5	6	3	2	2	10

Ques 12.

For the following transportation problem, find an initial basic feasible solution by North-West Corner method.

Factory	Ware house				Availability
		16	20	12	200
		14	8	18	160
		26	24	16	90
Demand		180	120	150

Starting from the solution obtained by North-West Corner method, find an optimal solution and the optimal transportation cost.

Ques 13.

A petrol station has a single pump and space for not more than 3 cars (2 waiting, 1
being served). Cars arrive according to a Poisson distribution at an average according
to a Poisson distribution at an average rate of 2 per minute. The service time has an
exponential distribution with an average rate of 4 per minute. Answer the following
questions: 
 i) Find the probability that an arriving car doesn’t have to wait.
 ii) Calculate the expected waiting time until a car is served and leaves the petrol
station. 

Ques 14.

A small project is composed of 8 activities where time estimates are listed in the table below:

Draw the project network diagram. Using the PERT find the expected time and variance for each activity.

Ques 15.

The time taken by a TV repair person to repair a TV set is exponentially distributed with mean 30 minutes. She repairs the sets in the order in which they come in. The arrival rate of the sets is approximately Poisson with an average rate of 10 per 8 hours day. Answer the following questions: (5)
 i) What is the repair person’s expected idle time each day?
 ii) How many jobs are ahead of the arriving set just brought in?
 iii) What is probability that there are 2 or more sets in the system?

Ques 16.

Find the shortest route using Bellman’s principle.

Ques 17.

Solve the following LPP by Simplex method:

such that

From the optimal table of the solution to the problem find the optimal solution of the dual of the problem. Verify complementary slackness property for the primal-dual pair.

Ques 18.

Use the dual simplex method to solve the following L.P.P.

Subject to

Ques 19.

Solve the following cost minimizing assignment problem.

Ques 20.

An investment company wants to study the investment proposals based on the profit factor. While analyzing a new investment proposal, the company estimated the probability distribution for the profit as follows:

Using the random numbers:

19, 7, 90, 2, 57, 28

Simulate the profit of the company for six trials.

Ques 21.

The production department for 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 ₹ 36 and the cost of carrying inventory is 25 percent of the investment in the inventories. The price of the raw material is  10 per kg.

 Determine the following:

i) Economic order quantity
ii) Optimal order cycle time and
iii) Minimum yearly inventory cost. 

Ques 22.

Listed in the table below are the activities and sequencing requirements necessary for the completion of a project.

i) Draw a net work diagram for the project.
ii) Find the critical path and the duration for the completion of the project. 

Ques 23.

Write the dual of the following LP problem:

Min.  

Subject to