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.

An insect of mass 20 g crawls from the centre to the outside edge of a rotating disc of mass 200g and radius 20 cm. The disk was initially rotating at 22.0 rads1 . What will be its final angular velocity? What is the change in the kinetic energy of the system?

. An automobile travelling at 80 km hr1 has tyres of radius 80 cm. On applying brakes, the car is brought to a stop in 30 complete turns of the tyres. What is the magnitude of the angular acceleration of the wheels? How far does the car move while the brakes are applie

A truck of mass 2000 kg moving on a highway experiences an average frictional force of 800 N. If its speed increases from 25 ms1 to 35 ms1 over a distance of 500 m, what is the force generated by the truck 

A bullet of mass 20 g, travelling at a speed of 350 ms1 , strikes a steel plate at an angle of 30º with the plane of the plate. It ricochets off at the same angle, at a speed of 320 ms1 . What is the magnitude of the impulse that the steel plate gives to the bullet? If the collision with the plate takes place over a time  s, what is the average force exerted by the plate on the bullet? 

A box of mass 50 kg is placed on an inclined plane. When the angle of the plane is increased to 30º, the box begins to slide downwards. Calculate the coefficient of static friction between the plane and the box. Draw the free body diagram.

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.