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 ComSwitch is currently trading for \( \$ 25 \) per share. If the takeovers occur, the financial advisor estimates that the price of Easterrn Cable will go to \( \$ 55 \) per share and ComSwitch will go to \( \$ 43 \) per share. There are four constraints by which the advisor is governed:
The client wants to invest at most \( \$ 50,000 \) .
Because of the the risk alternative associated with ComSwitch, the financial advisor has recommended that at most \( \$ 25,000 \) should be invested in ComSwitch.
Assume that the client wants to invest at least \( \$ 15,000 \) in Eastern Cable.
Assume that the client wants to invest at least \( \$ 10,000 \) in ComSwitch.
(a) Formulate a linear programming model for maximization of returns (with the assumption that the takeover will occur).