Question 548268
The other tutor apparently didn't understand what you want.
<pre>
We draw the lines

y=2x-8, y=10-x, y={{{(x+8)/2}}}, x=1, and y=2 

{{{drawing(400,400,-2,12,-2,12,

graph(400,400,-2,12,-2,12,2x-8,10-x,(x+8)/2,22,22,22,2), line(1,-5,1,15) )}}} 

Maximization 
Maximize p = 7x - 4y subject to
y &#8807; 2x - 8,  the red line y=2x-8 and the region above it, since it's y&#8807;
y &#8806; 10 - x, the green line y=10-x and the region below it, since it's y&#8806;
y &#8806; {{{(x + 8)/2}}}, the blue line y={{{(x+8)/2}}} and the region below it, since it's y&#8806;
x &#8807; 1, the black line x=1 and the region to the right of it, since it's x&#8807;
y &#8807; 2, the purple line y=2 and the region above it, since it's y&#8807;


We will chop off the unnecessary parts of the lines, leaving 
only the region bounded by them, which is this pentagon:

{{{drawing(400,400,-2,12,-2,12,

graph(400,400,-2,12,-2,12,22,22,22,22,22,22,2*(sqrt(x-1)/sqrt(x-1))(sqrt(5-x)/sqrt(5-x))), line(1,2,1,9/2) ,
blue(line(1,9/2,4,6)), green(line(4,6,6,4)), red(line(6,4,5,2))

 )}}} 

Now we must find all the corner points of this pentagon, by solving these
five systems:

{{{system(y=2x-8,10-x)}}} the red and green lines, which gives (6,4)
{{{system(y=2x-8,y=2)}}} the red and purple lines, which gives (5,2)
{{{system(x=1,y=2)}}} the black and purple lines, which gives (1,2)
{{{system(y=(x+8)/2,x=1)}}} the blue and black lines, which gives (1,4.5).
{{{system(y=10-x,y=(x+8)/2)}}} the blue and green lines, which gives (4,6)

{{{drawing(400,400,-2,12,-2,12,

graph(400,400,-2,12,-2,12,22,22,22,22,22,22,2*(sqrt(x-1)/sqrt(x-1))(sqrt(5-x)/sqrt(5-x))), line(1,2,1,9/2) ,
blue(line(1,9/2,4,6)), green(line(4,6,6,4)), red(line(6,4,5,2)),
locate(1,2,"(1,2)"), locate(6,4,"(6,4)"),locate(5,2,"(5,2)"),locate(4,6,"(4,6)"),locate(1,4.5,"(1,4.5)")

 )}}}
 
We evaluate p = 7x - 4y at each of those corner points:

Corner point | p = 7x - 4y
    (1,2)    |     -1
    (5,2)    |     27
    (6,4)    |     26
    (4,6)    |      4
  (1,4.5)    |    -11

So the maximum value of p=27 occurs when x=5 and y=2

Edwin</pre>