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I am struggeling with this problem:

Power Generation Company PowGen owns three generation units, each of them with the following cost function

Cost function

Consider the basic CED without losses (Ploss =0) and without generation limits.

a. What are the marginal cost functions for the three units?

b. Form the Lagrangian for the given decision (optimization) problem. Set up the necessary condition for a minimum of the CED problem. The only constraint to be considered is the demand constraint, which should be satisfied as an equality constraint. Consider 3 different situations for three specific system demand levels of Ptotal D: 5 MW, 30 MW and 80 MW (i.e. write three different Lagrangian functions down, each for different demand constraint). Use the method of Lagrange multipliers to solve the problem analytically.

I do not seem to know how to solve question B. I have looked up langrangian functions but do not know how to procceed. Could someone please help?

Thanks

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Maxioloco
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  • You seem to have been given someone's assigned exercise, but you have not digested what the problem is about. Passing the exercise along for other Readers to think through is not especially part of the mission of Math.SE, which is directed to learners of mathematics at all levels. For example, you "do not seem to know how to solve question B" but where did you get with part A? What is "the given decision (optimization) problem" that part B concerns? – hardmath Sep 22 '17 at 17:03
  • Hey,

    I got AiPGi + Bi PGI for question A and then using the values given respectively for A and B.

    I believe the optimization problem is that I have to get 5MW, 30 MW and 80 MW with these three generators. I just do not really know how to use Lagrangian functions here to calculate this. Hopefully you know more.

     – Maxioloco Sep 22 '17 at 17:39
  • Here is an introduction to posting mathematical notation. When $C_i$ is differentiated with respect to the amount $P_{G_i}$ of power generated, the result is $a_i + b_i P_{G_i}$ rather than what you got (for "marginal cost"). – hardmath Sep 22 '17 at 19:11

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