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

question 24

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?

---

Definitions:

Profit-Maximizing Level

The output level at which a firm achieves the highest possible profit, where marginal revenue equals marginal cost.

Marginal Revenue

The additional income earned by selling one more unit of a product or service.

Profit-Maximizing Level

The point at which a firm produces at a level where the difference between total revenue and total cost is the greatest.

Marginal Revenue

The additional income earned by selling one more unit of a good or service.