Give the corners of the feasible set: D=7x+20y subject to 2x +y less than equal to8 4x +6y less than equal 24 x greater than or equal to 0 y greater to or equal to 0 I already have my 6 points ... I need help figuring out if its a maximum or minimum

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Give the corners of the feasible set: D=7x+20y subject to 2x +y less than equal to8 4x +6y less than equal 24 x greater than or equal to 0 y greater to or equal to 0 I already have my 6 points ... I need help figuring out if its a maximum or minimum

Mathematics
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\[2x+y \le8 ...(1)\] \[4x+6y \le 24 \] \[or~2x+3y \le 12~~~...(2)\] consider 2x+y=8 x=0,y=8 y=0,x=4 so points are (0,8) and (4,0) again consider 2x+3y=12 x=0,y=4 y=0,x=6 so points are (0,4) and (6,0) \[x \ge0,y \ge0 \] graph lies in the first quadrant. put x=0,y=0 in (1) \[0+0\le 8 \] (0,0) lies in the graph of first line . similarly (0,0) lies in the graph of second line' 2x+y=8 2x+3y=12 subtract 2y=4,y=2 2x+2=8 2x=8-2=6 x=3 point of intersection is (3|dw:1441850946561:dw|,2) draw the graph
Oh great! that is exactly what I got. So if 8≤0+0 would I shade above my intersection? Also I got 80 for my max and 0 for my min.
(0,8) and (6,0) are not in the feasible region

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if\[2x+y \ge 8,0+0\ge8\] which is not true so (0,0) does not le on the graph so we had to shade right of this line
then only three points (4,0),(6,0) and (3,2)

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