Question 1175982
x = the number of hours working at store 1.
y = the number of hours working at store 2.


your constraint functions are:


x + y >= 18
x >= 5
x <= 13
y >= 6
y <= 11


your objective function appears to be total stress factor = 8x + 6y.
this is what you want to minimize.


using the desmos.com calculator, you would graph the opposite of the inequalities of the constraints.


your feasible region is the area on the graph that is not shaded.


you evaluate the objective function at each of the corner points.


the corner points with the smallest value gives you the minimum total stress factor.


the graph looks like this:


<img src = "http://theo.x10hosting.com/2021/022701.jpg" >


the corner point with the smallest stress factor is (7,11).
the total stress factor there is 122.


all the constraints are satisfied.


x = 7 which is greater than or equal to 5 and less than or equal to 13.
y = 11 which is greater than or equal to 6 and less than or equal to 11.
x + y = 18 which is greater than or equal to 18.


based on this evaluation, he should work 7 hours at store 1 and 11 hours at store 2 to minimize his total stress factor.