#$1$

Consider the following linear programming model with two decision variables, $x$ and $y.$

max,$xy$

$s.t.$

$,2x3y90$

$,2xy60$

$,x2y30$

$,x$

Use the graphical solution method to determine the optimal solution to this linear programming model: draw and label all constraints, identify the feasible region, draw a representative objective function, identify the optimal solution, and indicate the optimal objective function value.