This individual coursework will be issued on 26\'\" November for submission by F

Question

This individual coursework will be issued on 26'" November for submission by Friday. 11" December. It is worth 40X of the overall coursework mark. Feedback will be provided by solutions on Blackboard Learn. The coursework should be submitted as a Word Me to Blackboard Learn with answers, graphs and selected tables included. The document should be supported by any Excel and Matlab M files used. Formulate mathematical models in a variety of application areas and use them to solve problems of an appropriate level Integrale algebraic, graphical and numerical methods into modelling Demonstrate enhanced enterprise skills in such areas as problem solving and accessing information sources t communicate effectively. Initially two tanks each contain 50 liters of pure water. Coloured dye is then pumped into the first tank at a rate of 2 liters/minute, while pure water is pumped in to the second also at a rate of 2 liters/minute. Pumps exchange the mixture between the tanks at a rate of 6 liters/minute from tank 1 to tank 2 and at 4 liters/minute from tank 2 to 1. The diluted mixture is drawn off tank 2 at a rate of 4 liters/minute. It may be shown that the concentrations of dye in each tank at time f (minutes) satisfy the differential equations Draw a diagram illustrating the flows between the tanks. What are the initial conditions for these equations? Solve the above differential equations to obtain and as functions of time f Obtain a graph of concentrations against time. Use the differential equations directly to predict the steady state concentrations of the dye in each of the tanks. Investigate how the solution changes if the initial values of the concentrations are Explain the significance of each of the terms in the above differential equations in relation to the information given above. By exploring numerical values or an analytic solution investigate how the longer term value of the depends on rate of input of dye into tank 1. Is it possible for the concentrations in each tank to equalize after sufficient time? Justify your answer.

Explanation / Answer

1.

Barrier to entry is the restriction for new firms to enter into the market for producing or selling products.

If there is no barrier, like perfectly competitive market, entry has no restriction. New farms enter the market by seeing the other firms enjoying abnormal profits (Price > Average Total Cost). Once they enter, they create competition to pull down price and then enjoying such abnormal profits is no longer remained.

In order to minimize such competition barrier to entry is required. It happens to monopoly (with single seller) and oligopoly (with very few sellers) businesses. These businesses do not require completion for betterment of their products and/or prices, because either they are dealing with scare resources or social interests. Competition could damage their purpose.

If a market is dealing with scare resources like crude oil or coal, barrier to entry is important, because so many entries in this field could misuse such resources. Oligopoly is the best way of doing business in this market.

Barrier is important for protecting social interest. Utility services like water, electricity, etc should be under monopoly, since these are survival oriented. Needy people might not get price concession because of competition. Moreover people could be deprived or exploited. Therefore, barrier is needed.

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