Question 1137625
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Here is a picture of the feasibility region:<br>
{{{drawing(400,400,-4,20,-4,20,
line(-4,0,20,0),line(0,-4,0,20),red(line(-4,15,20,15)),green(line(0,20,20,0)),blue(line(8,-4,20,8)),
locate(-3,-1,"(0,0)"),locate(-3,16,"(0,15)"),locate(5,16,"(5,15)"),locate(17,4,"(16,4)"),locate(12,-1,"(12,0)"),
circle(0,0,.25),circle(0,15,.25),circle(5,15,.25),circle(16,4,.25),circle(12,0,.25)
)}}}<br>
The feasibility region is below the red and green lines and above the blue line.<br>
The equation of the red line is obviously y=15.<br>
A bit of algebra with the given points shows that the equation of the green line is y=-x+20 and the equation of the blue line is y=x-12.<br>
Since the feasibility region is below the red and green lines and above the blue line, the inequalities are<br>
{{{y <= 15}}}
{{{y <= -x+20}}}
{{{y >= x-12}}}<br>
The inequalities would probably be given in Ax+By form; that would be<br>
{{{y <= 15}}}
{{{x+y <= 20}}}
{{{x-y <= 12}}}<br>
(Note with the given information being the corners of the feasibility region, we can't tell whether the inequalities are "<" or "<=".)<br>