Question

Baking a tray of corn muffins takes cups 8 of milk and 5 cups of wheat flour. Baking a tray of bran muffins takes 4 cups of milk and 5 cups of wheat flour. A baker has 48 cups of milk and 35 cups of wheat flour. He makes ​$5 profit per tray of corn muffins and ​$3 profit per tray of bran muffins. How many trays of each type of muffin should the baker make to maximize his​ profit?

Answer 1

The baker make should make 5 trays of corn muffin and 2 trays of bran muffin to maximize his​ profit

How to determine how many trays of each type of muffin should the baker make to maximize his​ profit?

The given parameters can be represented in the following tabular form:

                        Corn Muffin (x)    Bran Muffin (y)    Total              

Milk                      8                          4                        48

Wheat flour          5                         5                        35

Profit                    5                          3

From the above table, we have the following:

Objective function:

Max P = 5x + 3y

Subject to:

8x + 4y <= 48

5x + 5y <= 35

x, y > 0

Express the constraints as equations

8x + 4y = 48

5x + 5y = 35

Divide 8x + 4y = 48 by 4 and divide 5x + 5y = 35 by 5

So, we have:

2x + y = 12

x + y = 7

Subtract the equations

2x - x + y - y = 12 - 7

Evaluate

x = 5

Substitute x = 5 in x + y = 7

5 + y = 7

This gives

y = 2

So, we have

x= 5 and y = 2

Hence, the baker make should make 5 trays of corn muffin and 2 trays of bran muffin to maximize his​ profit

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