Question

Johnson's Artisan Bakery is experimenting with two new croissant recipes. One recipe calls for 302.5 grams of bread flour and 30 grams of butter, while the other calls for 375 grams of bread flour and 43 grams of butter. The first recipe would yield $2.5 per croissant, and the second would yield $3.2 per croissant. Although the chefs like both recipes, they agree that since the second recipe requires more butter, they should probably only make half as much as the first. On a typical day, Johnson's would stock 20 kilograms of bread flour and 2 kilograms of butter. Formulate a linear programming model that maximizes the profit.

Answer 1

To maximize the profit, a linear programming model can be formulated. The model includes decision variables, an objective function, and constraints. The objective is to maximize profit (in dollars) by determining the number of croissants made using each recipe. The constraints are related to the availability of bread flour and butter, as well as minimum production quantities for each recipe.

Step-by-step explanation:

Linear Programming Model for Maximizing Profit:

To formulate a linear programming model that maximizes the profit, we need to define decision variables, objective function, and constraints.

Decision Variables:

Let x be the number of croissants made using the first recipe.
Let y be the number of croissants made using the second recipe.

Objective Function:

Maximize Z = 2.5x + 3.2y (profit in dollars)

Constraints:

1. 302.5x + 375y ≤ 20000 (bread flour constraint)
2. 30x + 43y ≤ 2000 (butter constraint)

Non-negativity Constraints:

x ≥ 20 (since the first recipe should yield at least 20 croissants)
y ≥ 10 (since the second recipe should yield at least 10 croissants)

Final Linear Programming Model:

Maximize Z = 2.5x + 3.2y
subject to
302.5x + 375y ≤ 20000
30x + 43y ≤ 2000
x ≥ 20
y ≥ 10
where x and y are non-negative integer variables.