Hello, offthewake!
These are "linear programming" problems.
I'll babystep through the second one . . .
An accounting firm has 1350 hours of staff time
and 322 hours of reviewing time available each week.
The firm charges $140 for an audit and $35 for a tax return.
Each audit requires 90 hours of staff time and 14 hours of review time.
Each tax return requires 15 hours of staff time and 7 hours of review time.
What number of audits and tax returns will yield the maximum revenue?
What is the maximum revenue?
Make a table of the data . . .
. .
Let: .
The table becomes:
. .
. . Revnue: .
Reading down the columns, we find our inequalities:
. .
Now we graph the four inequalities.
[1] and [2] places us in Quadrant 1.
To graph , graph the line: .
. . and shade the region below it.
Its intercepts are: (15,0) and (0,90).
. . Plot the intercepts, draw the line, shade the region below the line.
To graph , graph the line: .
. . and shade the region below it.
Its intercepts are: (23,0) and (0,46).
. . Plot the intercepts, draw the line, shade the region below the line.
The graph will look like this: Code:

90 *
*
 *
 *
 *
 *
46 o *
:::* *
:::::::o
::::::::* *
:::::::::* *
::::::::::* *
  o      o      *  
0 15 23
We are concerned with the vertices of the shaded region.
We can see three of them: .
The fourth vertex is the intersection of the two slanted lines.
Solve the system: .
. . Hence, the fourth vertex is: .
Finally, test the four vertices: .
. . in the Revenue function to see which produces maximum revenue.