A financial advisor at Paul & Job Ltd. identified two companies that are likely candidates for a takeover in the near future.Asian TV is a leading manufacturer of flexible cable systems used in the construction industry and Switchering is a new firm specializing in digital switching systems Asian TV is currently trading for $40 per share, and Switchering is currently sharing for $25 per share.If the takeovers occur, the financial advisor estimates that the price of Asian TV will go to $55 per share and Switchering will go to $43 per share.At this point in time, the financial advisor has identified Switchering as the higher-risk alternative.Assume that a client indicates a willingness to invest a maximum of $50,000 in the two companies.The client wants to invest at least $15,000 in Asian TV and at least $10,000 in Switchering.Because of the higher risk associated with Switchering, the financial advisor has recommended that at most $25,000 should be invested in Switchering.

a.Formulate a linear programming model that can be used to determine the number of shares of Asian TV and the number of shares of Switchering that will meet the investment constraints and maximize the total return for the investment.(12 marks)

b.By using your own graph paper, solve the linear programmingproblem with the graphical method. Label constraint lines clearly, shade the feasible region.The graph may be drawn to the following scale of 500 units to 2cm. Show evidence of working to arrive at the solution. (10 marks)

c. Determine the coordinates of each extreme point(4 marks)

d. Find the optimal solution. State the maximum total return.(4 marks )