In the class lectures, two simple power optimization problem were discussed in the context of linear...

 

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In the class lectures, two simple power optimization problem were discussed in the context of linear programming (LP): a) No generator up-limits; no loss; b) With generator up-limits; no loss; Now, we consider a slightly generalized problem: c) With generator up-limits; with loss. This problem can be expressed as follows: minimize z= (a + b₂P₁); $1. Σ P₁ = P + P₁; k=1 (1) P₁ = Boo + Box P (2) Pmin SP SPmax (k=1,2,....n) In (1) and (2), PL, Boo, and Box are constants. Q1 (10 points). Convert the above problem into the standard form (SF) of LP. You must use the definition of SF in the textbook. Q2 (10 points). Express the SF by matrices. In the class lectures, two simple power optimization problem were discussed in the context of linear programming (LP): a) No generator up-limits; no loss; b) With generator up-limits; no loss; Now, we consider a slightly generalized problem: c) With generator up-limits; with loss. This problem can be expressed as follows: minimize z= (a + b₂P₁); $1. Σ P₁ = P + P₁; k=1 (1) P₁ = Boo + Box P (2) Pmin SP SPmax (k=1,2,....n) In (1) and (2), PL, Boo, and Box are constants. Q1 (10 points). Convert the above problem into the standard form (SF) of LP. You must use the definition of SF in the textbook. Q2 (10 points). Express the SF by matrices.