A bake sale is organized to raise funds for a school club on Valentine's Day. The bake sale offers two types of
baked goods: cupcakes and cookies. Each cupcake costs $0.50 to make and can be sold for $2.00, while each
cookie costs $0.30 to make and can be sold for $1.50. The bake sale has a limited budget of $150 to purchase
ingredients and a maximum of 300 baked goods that can be sold. Determine how many of each good needs to be
baked in order to maximize the revenue given the constraints.
Solution:
Let x = number of cupcakes and y = number of cookies
The objective is to maximize revenue, which is given by the equation:
Revenue = 2x + 1.5y
The constraints are:
0.5x + 0.3y ≤ 150 (budget)
x + y ≤ 300 (maximum number of baked goods)
x ≥ 0, y ≥ 0 (non-negativity)
Using the simplex method, the optimal solution is x = 200 and y = 100. This means that 200 cupcakes and 100 cookies should be baked in order to maximize the revenue given the constraints.