Find the shortest route using Bellman’s principle.

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?

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.

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. 

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.

Write a note on democracy and elections.

Examine representative democracy.

Write a note on type of democracy.

Examine Jacques Derrida’s views on Post –Modernism.

Write a note on the Second Wave of feminist political theory.

What is Conservatism? Explain with reference to the views of Edmund Burke.

What do you understand by Evolutionary and Revolutionary Socialism? Elaborate.

Write a note on Modern Liberalism / Welfarism. 

Explain Ralph Miliband’s views on the state.

Discuss the revival of political theory.

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

) 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.

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.

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:

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?