The Pat$-$A$-$Cake Pastry Sbop makes chocolate cake in three sizes $-$ Small, Medium, and Large. The shop has the following amounts of the throe main ingredients

on hand$-400$ ounces of cake flour, $550$ ounces of caster sugar, and $150$ ounces of cocon powder. The table below provides details on the amount of each

ingredient required for each cake size as well as the profit contributions.

Develop and solve a linear programming model to maximize the profit. What is the opstmal solution for this problem?