Question

P=-30x+25y

Subject to 2x+3y>=30
2x+y<=26
-6x+5y<=50
x,y>=0

I need the minimize and maximaze

Answer 1

One point at the origin, constrained to first quadrant.

first constraint #1
2x+3y>=30
when x = 0, y = 10
when x = 15, y = 0
area above that line is in our region (are you sure your arrow is correct?)

second constraint #2
2x+y<=26
when x = 0, y = 26
when x = 13, y = 0
area below that line is in

third constraint #3
-6x+5y<=50
when x = 0, y = 10
when x = -50/6 or -8 1/3 , y = 0
area below that line is in

sketch a graph. You see that our region of interest is a triangle from (0,10) to the intersection of #2 and #3 down to the intersection of #1 and #2
first #1 and #2
2x+3y=30
2x+y=26
gives
2 y = 4 or y = 2 then x = 12
so (12,2)
now #2 and #3
2x + y=26 -->6 x + 3y = 78
-6x+5y=50
gives
8y = 128
y = 16 then x = 5
so (5,16)
NOW
calculate P at (5,16) and (12,2) and (0,10) and chose the biggest or smallest whichever you want. If P is "profit", you probably want the biggest.