Algebra : Cooking Problem. Read inside please. =)?

Question

Baking a tray of corn muffins takes 4 cups of milk and 3 cups of wheat flour. A tray of bran muffins takes 2 cups of milk and 3 cups of wheat flour. A baker has 16 cups of milk and 15 cups of wheat flour. He makes $3 profit per tray of corn muffins and $2 profit per tray of bran muffins. How many trays of each type of muffin should the baker make to maximize his profit.



Ok, this is a linear programming problem. I came out with 3 trays of corn muffins and 2 trays of bran muffins to maximize profit. Could someone do this problem and verify the answer for me.

Help is much appreciated. =)

Answer 1

Step 1: Determine how the profit correlates to the ingredients used.
First, notice that the corn muffins and bran muffins use the same amount of wheat. Therefore, you can ignore wheat flour, except how it limits how many trays you can make.

So, there's $2 profit for 2 cups of milk used, and $3 for 4 cups of milk used. Thus, one should bake bran muffins if wheat is a limiting factor, and corn if it is not.

Step 2: Determine at what point wheat is a limiting factor:
There are 5 total trays you can make (15 total cups, 3 cups/tray).
Write that as c + b = 5
You have 16 cups of milk, and corn muffins require 4, bran muffins require 2. Write that as 4c + 2b = 16

Step 2: Substitute one variable and solve:
c + b = 5
b = 5 - c
4c + 2b = 16
4c + 2(5-c) = 16
4c - 2c + 10 = 16
2c = 6
c = 3

Thus, you are correct: use 3 trays of corn muffins, 2 trays of bran muffins.

Answer 2

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