The Primo Insurance Company is introducing two new product lines: special risk insurance and mortgages. The expected profit is $$5$ per unit on special risk insurance and $$2$ per unit on mortgages. Management wishes to establish sales quotas for the new product lines to maximize total expected profit. The work requirements are as follows:

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$($a$)$ Formulate a linear programming model for this problem.

$($b$)$ Use the graphical method to solve this model.

What is the maximum profit $($z$),$ number of units of special risk insurance $($x$),$ and number of units of mortgages $($y$)?$