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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?

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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.

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    So then why shouldn't I change my answer if it's impossible to solve?2012-12-09