The Pat-A-Cake Pastry Shop Makes Chocolate Cake in Three Sizes

Essay

The Pat-A-Cake Pastry Shop makes chocolate cake in three sizes - Small, Medium, and Large. The shop has the following amounts of the three main ingredients on hand - 400 ounces of cake flour, 550 ounces of caster sugar, and 150 ounces of cocoa powder. The table below provides details on the amount of each ingredient required for each cake size as well as the profit contributions. $$\begin{array} { l c c c c } \text { Cake } & \text { Small } & \text { Medium } & \text { Large } & \text { Available } \\\hline \text { Plain flour (Ounce) } & 8 & 16 & 21 & 400 \\\text { Caster sugar (Ounce) } & 18 & 22 & 25 & 550 \\\text { Cocoa powder (Ounce) } & 3 & 5 & 11 & 150 \\\hline \text { Profit/Unit } & \$ 18 & \$ 25 & \$ 32 &\end{array}$$ Develop and solve a linear programming model to maximize the profit. What is the optimal solution for this problem?