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# Mathematics - Linear Operators

A financial advisor at Diehl Investments identified two companies that are likely candidates for a takeover in the near future. Eastern Cable is a leading manufacturer of flexible cable systems used in the construction industry and ComSwitch is a new firm specializing in digital switching systems. Eastern Cable is currently trading for \$40 per share and Com-
Switch is currently trading for \$25 per share. If the takeovers occur, the financial advisor estimates that the price of Eastern Cable will go to \$55 per share and ComSwitch will go to \$43 per share. At this point in time, the financial advisor identified ComSwitch as the higher risk alternative. Assume that a client who indicated a willingness to invest a maximum of \$50,000 in the two companies wants to invest at least \$15,000 in Eastern Cable and at least \$10,000 in ComSwitch. Because of the higher risk associated with ComSwitch, the financial advisor recommends that at most \$25,000 should be invested in ComSwitch.

a. Formulate a linear programming model that can be used to determine the number of
shares of Eastern Cable and the number of shares of ComSwitch that will meet the investment constraints and maximize the total return for the investment.
b. Graph the feasible region.
c. Determine the coordinates of each extreme point.
d. Find the optimal solution.

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