Maximizing profit, is a way of getting the highest possible profit, from a function.
The bakery should make 45 loaves of A and 0 loaves of B, to maximize profit
To do this, we make use of the following representations.
x represents source A, and y represents source B
So, we have:
<u>Constraint 1: </u>
A uses 5 pounds, and B uses 2 pounds of oats.
Available: 180
The above condition is represented as;
![\mathbf{5x + 2y \le 180}](https://tex.z-dn.net/?f=%5Cmathbf%7B5x%20%2B%202y%20%5Cle%20180%7D)
<u>Constraint 2: </u>
A and B use 3 pounds of flour each.
Available: 135
The above condition is represented as;
![\mathbf{3x + 3y \le 135}](https://tex.z-dn.net/?f=%5Cmathbf%7B3x%20%2B%203y%20%5Cle%20135%7D)
<u>Objective function</u>
A yields $40, while B yields $30
So, the objective function is:
![\mathbf{Maximize\ Z = 40x + 30y}](https://tex.z-dn.net/?f=%5Cmathbf%7BMaximize%5C%20Z%20%3D%2040x%20%2B%2030y%7D)
So, we have:
![\mathbf{Maximize\ Z = 40x + 30y}](https://tex.z-dn.net/?f=%5Cmathbf%7BMaximize%5C%20Z%20%3D%2040x%20%2B%2030y%7D)
Subject to
![\mathbf{5x + 2y \le 180}](https://tex.z-dn.net/?f=%5Cmathbf%7B5x%20%2B%202y%20%5Cle%20180%7D)
![\mathbf{3x + 3y \le 135}](https://tex.z-dn.net/?f=%5Cmathbf%7B3x%20%2B%203y%20%5Cle%20135%7D)
![\mathbf{x,y \ge 0}](https://tex.z-dn.net/?f=%5Cmathbf%7Bx%2Cy%20%5Cge%200%7D)
See attachment for the graph of the subjects
From the graph, we have the corner points to be:
![\mathbf{(x,y) = \{(0,45),(30,15),(45,0)\}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%28x%2Cy%29%20%3D%20%5C%7B%280%2C45%29%2C%2830%2C15%29%2C%2845%2C0%29%5C%7D%7D)
Substitute these values in the objective function
![\mathbf{Z = 40(0) +30(45) = 1350}](https://tex.z-dn.net/?f=%5Cmathbf%7BZ%20%3D%2040%280%29%20%2B30%2845%29%20%3D%201350%7D)
![\mathbf{Z = 40(30) +30(15) = 1650}](https://tex.z-dn.net/?f=%5Cmathbf%7BZ%20%3D%2040%2830%29%20%2B30%2815%29%20%3D%201650%7D)
![\mathbf{Z = 40(45) +30(0) = 1800}](https://tex.z-dn.net/?f=%5Cmathbf%7BZ%20%3D%2040%2845%29%20%2B30%280%29%20%3D%201800%7D)
The maximum value of Z is at: (45,0)
This means that: the bakery should make 45 loaves of A and 0 loaves of B, to maximize profit
Read more about maximizing functions at:
brainly.com/question/14728529