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I have a question about some stochastic linear programming formulas, namely (4.3),(4.4),(4.5) and (4,6) in the snippet below. I do not follow how was created the argument of $c$ in (4.3), the formula (4.4) and from (4.4) the formula (4.5), and finally (4.6). I'm looking on it almost a week without any success.

The snippet is taken from the book Introduction to stochastic programming by John Birge,the second edition. enter image description here

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My reputation it too low to add a comment, so don't take this as an answer rather than comment.

What exactly is your problem?

Those (4.3-4.5) are just assumptions/pre-conditions to give a real sounding problem/illstration. And those assumptions are summarized into the optimization problem (4.6). c is a new variable introduced which is (later) used for optimization purposes.

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  • $\begingroup$ Thank you for your interest. My problem is how $\frac{w\cdot \pi \cdot x^2}{4}$ was created. And also both sides of the inequality $\frac{w}{\xi^3}\leq 39.27$ was created. And finally $\frac{w^3}{\xi^4}\leq 63,169$ and $Q(w,x,\xi)$. Just as I've said in my OQ, all the (,)'s. Are they all just ilustration examples with no rule ? Is $c$ a variable or rather a function in (4.3) ? $\endgroup$ – user3357120 Sep 25 '19 at 18:32

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