Possible misstake in question?

[Guest]

Hello, so there's a graph provided in the task which I'm trying to solve for a quite a while and I am really confused where the 5 to 8 line came from, because (5x+8y<5) doesn't create that sort of line. Is it possible that there's a misstake done by my teacher or am I understanding something wrong?

[HallsofIvy]

Yes, something is wrong. The region where [tex]5x+ 8y\le 5[/tex], x>0, y> 0, is bounded by the x and y axes and by the line 5x+ 8y= 5. When y= 0, x= 1 so that line goes through the point (5, 0), not (8, 0) and when x= 0, y= 5/8 so that line goes through the point (0, 5/8), not (0, 5). The line that passes through (8, 0) and (0, 5) is 5x+ 8y= 40, not 5x+ 8y= 5.