# Are these linear programming constraints correct?

The problem is: Beth works a maximum of $$20$$ hours/week programming computers and tutoring math. She receives $$\25$$/hour for programming and $$\20$$/hour for tutoring. She works between $$3$$ and $$8$$ hours/week programming, but always gives more time to tutoring. How many hours should she work at each job to maximize her income?

Let $$x$$ = # hours programming and $$y$$ = # hours tutoring.

My constraints are:

Total hours: $$x + y ≤ 20$$

Hours programming: $$3 ≤ x ≤ 8$$

Hours tutoring: $$y > x$$

Are these right?

• Seems OK. I would be more comfortable with $y\ge x$, even though it goes against the usual meaning of "more". Dec 3, 2012 at 20:40
• But then y could be equal to x, and y is always greater. Dec 3, 2012 at 20:41
• Sure. But if you are ultimately solving "graphically," and the relevant corner involves the line $y=x$, we probably would not reject that as an answer. Dec 3, 2012 at 20:48
• But if I'm solving graphically, I would use the vertices, no? So it wouldn't matter if the line was y ≥ x or y > x since it would be the same line. Dec 3, 2012 at 20:50
• Don't worry about it. Dec 3, 2012 at 20:52