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A clever, but ethically corrupted, mathematics student used to sell assignment solutions to her lazy fellow students. The student, however, learned that she can make much more money by charging the students fees for doing the assignments with them.

This semester the students need to complete three assignments:

  • One in Statistical Models
  • One in Introduction to Partial Differential Equations
  • One very difficult one in Optimization and Financial Mathematics

It takes 2 hours to explain the assignment to one student for Statistical Models, 1/2 hours for Introduction to Partial Differential Equations and 5 hours for Optimization and Financial Mathematics. The student can charge \$5, \$0.50, and \$10 per hour for Statistical Models, Introduction to Partial Differential Equations and Optimization and Financial Mathematics, respectively.

In Statistical Models there are not more than 10 students wanting her service. In Introduction to Partial Differential Equations there are more than 50 students wanting her service and she has obligations to take at least 50. In Optimization and Financial Mathematics,the course with the most diligent students, there are not more than 2 students wanting her service.

How many students from each course will the clever student offer her service to maximize her profit, if she does not want to spend more than 50 hours on the assignments?

(a) Formulate this as a linear programming problem

(b) Solve the problem using the two-phase simplex algorithm.

I do not know how much should I charge, because it is my first time to ask a question here. I am so sorry about this, but I am really need to know the solution.

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    $\begingroup$ How much is she charging for the solution to this problem? $\endgroup$ Aug 31, 2016 at 15:27
  • $\begingroup$ I do not know how much should I charge, because it is my first time to ask a question here. I am so sorry about this, but I am really need to know the solution. $\endgroup$
    – Dong YE
    Aug 31, 2016 at 15:30
  • $\begingroup$ I am studying Optimization and Financial Mathematics by myself, I found this question is challenge for me. $\endgroup$
    – Dong YE
    Aug 31, 2016 at 15:32

1 Answer 1

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A good way to start a problem such as this is to identify the variables, then the objective and constraints. What quantities does the question ask for? What objective is being maximized or minimized? Then see how you can express the objective and constraints in terms of these variables, and perhaps others.

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  • $\begingroup$ In fact, I know how to solve part a, but part b is a little hard for me $\endgroup$
    – Dong YE
    Sep 1, 2016 at 1:41

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