Systems, Matrices, and Determinants · Hard problem

Application. A bakery makes muffins ($x$) and scones ($y$). Oven time gives $2x+y\le12$; dough supply gives $x+y\le8$; and $x,y\ge0$. Profit is $z=5x+4y$ dollars. How many of each maximizes profit, and what is the maximum?