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 . . .
. . $\displaystyle \begin{array}{ccc}
& \text{Staff} & \text{Review} \\ \hline \hline
\text{Audits} & 90 & 14 \\ \hline
\text{Taxes} & 15 & 7 \\ \hline \end{array}$
Let: .$\displaystyle \begin{array}{ccccc}x &=& \text{no. of audits,} & x \geq 0 & [1]\\ y &=& \text{no. of taxes,} & y \geq 0 & [2] \end{array}$
The table becomes:
. . $\displaystyle \begin{array}{ccc}
& \text{Staff} & \text{Review} \\ \hline \hline
\text{Audits} & 90x & 14x \\ \hline
\text{Taxes} & 15y & 7y \\ \hline \hline
\text{Total} & 1350 & 322 \end{array}$
. . Revnue: .$\displaystyle R \;=\;140x + 35y$
Reading down the columns, we find our inequalities:
. . $\displaystyle \begin{array}{cccccccc}90x + 15y & \leq 1350 & \Rightarrow & 6x + y & \leq & 90 & [3]
\\ 14x + 7y & \leq 322 & \Rightarrow & 2x + y & \leq & 46 & [4] \end{array}$
Now we graph the four inequalities.
[1] and [2] places us in Quadrant 1.
To graph $\displaystyle 6x + y \:\leq\:90$, graph the line: .$\displaystyle 6x + y \:{\color{red}=}\:90$
. . 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 $\displaystyle 2x + y \:\leq \:46$, graph the line: .$\displaystyle 2x + y \:{\color{red}=}\:46$
. . 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: .$\displaystyle (0,0),\:(15,0),\:(0,46)$
The fourth vertex is the intersection of the two slanted lines.
Solve the system: .$\displaystyle \begin{array}{ccc}6x + y &=& 90 \\ 2x+ y &=& 46\end{array}\quad \Rightarrow\quad \begin{array}{c}x \:=\:11 \\ y \:=\:24 \end{array}$
. . Hence, the fourth vertex is: .$\displaystyle (11,24)$
Finally, test the four vertices: .$\displaystyle (0,0),\;(14,0),\;(0,46),\;(11,24)$
. . in the Revenue function to see which produces maximum revenue.