$(30$ pts$.)$ The research and development division of a company has been developing four possible new product lines. Management must make a decision as to which of these four products actually will be produced and at what levels. Therefore, they have asked the OR department to formulate a mathematical programming model to find the most profitable product mix. A substantial cost is associated with beginning the production of any product, as given in the first row of the following table. The marginal net revenue from each unit produced is given in the second row of the table. The third row indicates the maximum amount of each product that can be produced.

$\backslash$table$[[$Product$,1,2,3,4$