Question

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

Answer 1

\[2x+y \le8 ...(1)\]
\[4x+6y \le 24 \]
\[or~2x+3y \le 12~~~...(2)\]
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 (3,2)
draw the graph

Answer 2

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.

Answer 3

(0,8) and (6,0) are not in the feasible region

Answer 4

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

Answer 5

then only three points (4,0),(6,0) and (3,2)