Question

1. A large-scale corporate bakery needs to determine how many of their three bestselling products they can make each day. Their bagels require 9 minutes to prepare, 22 minutes to bake, and 6 minutes to wrap. Their lemon bars require 12 minutes to prepare, 24 minutes to bake, and 8 minutes to wrap. Their sourdough loaves require 15 minutes to prepare, 28 minutes to bake, and 8 minutes to wrap. Across all of their employees’ labor-hours per day, they have 80 hours of preparation time available, 160 hours of baking time available, and 48 hours of wrapping time available. How many of each product can be made each day? (Use Gauss-Jordan Elimination Method with an augmented matrix to solve).

Answer 1

Let's assume

Number of bagels =x

Number of lemon bars=y

Number of sourdough loaves=z

now, we can find system of equations

Preparation time equation:

Baking time equation:

Wrapping equation:

so, we get system of equations as

now, we can find augmented matrix

now, we can change into reduced row-echelon form

step-1:multiply the 1st row by 1/9

step-2: add -22 times the 1st row to the 2nd row

step-3: add -6 times the 1st row to the 3rd row

step-4:multiply the 2nd row by -3/16

step-5:multiply the 3rd row by -1/2

step-6: add -13/8 times the 3rd row to the 2nd row

step-7: add -5/3 times the 3rd row to the 1st row

step-8: add -4/3 times the 2nd row to the 1st row

so, we get

............Answer