Question 1131670
Your information is confusing. 
You have {{{y>=2}}} and {{{y>=0}}}.
I'll assume {{{y>=2}}}
.
.
.
{{{4x+4y<=48}}}
{{{x+y<=12}}}
.
.
.
*[illustration d3.JPG].
.
.
.
{{{x+2y<=20}}}
.
.
.
*[illustration d4.jpg].
.
.
.
Putting them together,
.
.
.
 *[illustration d5.JPG].
.
.
.
Check the function for a maximum at each of the three vertices,
(0,10)
(10,2)
(4,8)
I'll do one, you do the other two,
{{{P=3x+54y}}}
So at (0,10),
{{{P(0,10)=3(0)+54(10)=0+540=540}}}
Now do the same for the other two.