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

maxx $y$

$s.t.$

$2x3y90$

$2xy60$

$x2y30$

$x15$

$x,y>0$

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.