Hello again, daniel4616!
Here's #6 . . . in babysteps . . .
6. Maximize
subject to:
We must graph and shade the inequalities.
places us in the first quadrant.
Graph the line:
It has intercepts: . . Sketch the line.
Solve for and note the inequality: .
Since the inequality is , shade the region below the line. Code:
 *:
 *::::
 *:::::::
2*::::::::::
* :::::::::::
  *  +        
2 
Graph the line
It has intercepts:
Since we have: , we shade below the line. Code:

18*
*
:*
::*
:::*
::::*
:::::*
::::::*
 +    * 
 6
Of course, we graph these region on the same graph.
And the final shaded region looks like this.
(Note the vertices of the region.) Code:

 *(4,6)
 *::*
(0,2)*:::::*
:::::::*
  *     *  
(0,0) (6.0)
We find the intersection of the two slanted lines
. . by solving the system:
and we get:
The vertices are the only "critical values" we are concerned with.
Test them in the zfunction to see which gives a maximum value.
Answer: . to maximize .
