Question

A baking tray of corn muffins takes 3c milk and 4c flour. A tray of bran muffins takes 4c milk and 2c flour. A baker has 24c milk and 16c flour. He makes $3.25 profit per tray of corn and $2.75 profit per tray of bran muffins. How many trays of each type of muffin should he bake to get maximum profit?

Answer 1

To maximize profit, formulate a linear optimization model with the profit function P = 3.25x + 2.75y under the constraints of available milk and flour. Solve the linear programming model using graphical methods or software.

Step-by-step explanation:

To maximize profit from baking corn and bran muffins given the constraints on milk and flour, we can formulate the problem as a linear optimization model. Let's denote the number of trays of corn muffins as x and the number of trays of bran muffins as y.

The profit function we want to maximize is P = 3.25x + 2.75y, representing the profit per tray of corn and bran muffins, respectively.

Given the constraints on milk and flour, we have:

• 3x + 4y ≤ 24 (milk constraint)
• 4x + 2y ≤ 16 (flour constraint)

We also have the non-negativity constraints:

• x ≥ 0
• y ≥ 0

Using these constraints, we can initiate a linear programming model to find the values of x and y that will maximize P. This usually requires graphical methods or the use of software that implements the simplex algorithm or another method suitable for linear programming.

After solving the set of equations, we would get the ideal number of trays for corn muffins and bran muffins that would yield the maximum profit within resource limitations.