this table makes it easier to see how the variables are applied to the problem.
x = the number of audits.
y = the number of returns.
x y
audits returns
staff hours 100 12.5 <= 800
review hours 8 2 <= 96
revenue dollars 1000 300 maximize
your constraint inequalities are:
100x + 12.5 <= 800 for staff hours
8x + 2y <= 96 for review hours
your objective function is:
1000x + 300y for revenue dollars that you want to maximize
using the desmos.com calculator, you graph the opposite of the constraint inequalities.
you will graph:
100x + 12.5 <= 800 for staff hours
8x + 2y <= 96 for review hours
also graph:
x <= 0
y <= 0
this is because x and y must be greater than or equal to 0 in this problem.
the area on the graph that is NOT shaded is the region of feasibility.
your maximum revenue will be at the corner points of this region.
you evaluate your objective function at those corner points.
here's what the graph looks like.
you will find that your maximum revenue is at the point (0,48).
the revenue is 0x + 300y = 0 + 14,400 = 14,400.
that means max revenue when you provide zero audits and 48 tax returns for revenue of 14,400 dollars.
your constraint inequalities need to be satisfied.
at (0,48), 100x + 12.5y = 600 <= 800, and 8x + 2y = 96 <= 96.
the constraints are all satisfied.
your maximum revenue is 14,400.
you can evaluate the other corner points on your own to confirm that (0,48) give you the maximum revenue.
the constraints should also be saisfied at those other corner points as well.