Question 1184772
x = number of loaves of whole wheat bread.
y = number of loaves of cheese bread.


objective function:
maximize profit of 2.1 * x + y
constraints:
x,y >= 0
x + y <= 120
1.5x + y <= 165
1/3 * x + 1/2 * y <= 55


with the desmos.com calculator:


graph the opposite of the inequalities.
the region of feasibility is the area of the graph  not shaded.
evaluate each corner point of the feasible region with the objective function.
the solution will be at one of the corner points.


the graph looks like this:


<img src = "http://theo.x10hosting.com/2021/092301.jpg" >


the profit at:


(0,110) = 0 * 1.2 + 110 * 1 = 110
(30,90) = 30 * 1.2 + 90 * 1 = 126
(90,30) = 90 * 1.2 + 30 * 1 = 138 *****
(110,0) = 110 * 1.2 + 0 * 1 = 132


the maximum profit is at (90,30)


all the constraints are met.


x,y are both >= 0
x + y = 90 + 30 = 120 <= 120
1.5x + y = 165 <= 165
1/3x + 1/2y = 30 + 15 = 45 <= 55


solution is (x,y) = (90,30) = 138


that means 90 loaves of whole wheat bread and 30 loaves of cheese bread for maximum profit.


when the profit of cheese bread goes from 1 to 1.5, you get:


(0,110) = 0 * 1.2 + 110 * 1.5 = 165
(30,90) = 30 * 1.2 + 90 * 1.5 = 171 *****
(90,30) = 90 * 1.2 + 30 * 1.5 = 153
(110,0) = 110 * 1.2 + 0 * 1.5 = 132



the maximum profit is now at (x,y) = (30,90) = 171.


that means 30 loaves of whole wheat bread and 90 loaves of cheese bread for maximum profit.


the graph is the same because none of the constraints has changed.


the only change is the evaluation of the objective function at each of the corner points.