Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

The problem is: Beth works a maximum of 20 hours/week programming computers and tutoring math. She receives 25 dollars/hour for programming and 20 dollars/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

My objective function is:

25x + 20y = maximum profit

Here is my graph:

Here is my graph:

And from looking at the corner points, I can say that the answer is 8 hours programming and 12 tutoring. Is this plus all my other work correct?

share|improve this question
add comment

1 Answer

up vote 1 down vote accepted

Yes, your optimal value is correct (even MATLAB agree). Althougt constraints with strict inequalities doesn't make a very good sense in LP (your hour tutoring constraint), there should be >= to make it LP problem. In this formulation the optimal value would not be on the corner of the polytope.

share|improve this answer
    
What is a sharp inequality? –  Someone Dec 9 '12 at 20:59
    
Sorry, I meant strict inequality. –  qmsource Dec 9 '12 at 21:01
    
So sorry, I don't really understand why it doesn't make sense. –  Someone Dec 9 '12 at 21:02
    
For example the value of the x would not be bounded. You could make it go infinitely close to y value, so there would not be a final value. Because of this, the LP problems dont allow sharp inequalities (see en.wikipedia.org/wiki/Linear_programming) –  qmsource Dec 9 '12 at 21:06
1  
@Someone just to make it clear, the reason is that when you say "$y>x$", you're saying "$y\ne x$". That's no good as we can see from the following ridiculous LPP: $\max z$ subject to $z<1$. As you can see, there is no solution. Why? Well $z$ can't be 1 cause $z<1$. But there is no next smallest number under 1, at least not in the real numbers. So strict inequalities make LPP's impossible to solve. –  crf Dec 9 '12 at 22:03
show 6 more comments

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.