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+//exa 2.22

+clc;clear;close;

+format('v',10);

+//F1=0.05*P1^2+21.5*P1+800;//Rs./hr

+//F2=0.1*P2^2+27*P2+500;//Rs./hr

+//F3=0.07*P3^2+16*P3+900;//Rs./hr

+PT=200;//MW

+Pmax=120;//MW

+Pmin=39;//MW

+//coefficients : 

+c1=0.05;c2=0.1;c3=0.07;

+b1=21.5;b2=27;b3=16;

+a1=800;a2=500;a3=900;

+lambda=(1/2*[b1/c1+b2/c2+b3/c3]+PT)/[1/2*[1/c1+1/c2+1/c3]];

+//Economical loading dF1/dP1=dF2/dP2=dF3/dP3

+P1=poly(0,'P1');P2=poly(0,'P2');P3=poly(0,'P3');

+dF1bydP1=2*0.05*P1+21.5;

+dF2bydP2=2*0.1*P2+27;

+dF2bydP3=2*0.07*P3+16;

+//Solving equation :

+A=[2*0.05 0 0;0 2*0.1 0;0 0 2*0.07];

+B=[lambda-21.5;lambda-27;lambda-16];

+X=A^-1*B;

+P1=X(1);//MW

+P2=X(2);//MW

+P3=X(3);//MW

+if P2<Pmin then

+    P2=Pmin;

+end

+P1plusP3=PT-P2;//MW

+//dF1/dP1=dF3/dP3

+//Let loads are P1 & P1plusP3-P1

+clear('P1','P3');

+P1=poly(0,'P1');P3=poly(0,'P3');

+ eqn=2*0.05*P1+21.5-2*0.07*(P1plusP3-P1)-16;

+ P1=roots(eqn);//MW

+ P3=P1plusP3-P1;//MW

+ disp("Optimum scheduling :");

+ disp(P3,P2,P1,"Loads P1, P2 & P3 in MW are :");

+ F1=0.05*P1^2+21.5*P1+800;//Rs./hr

+F2=0.1*P2^2+27*P2+500;//Rs./hr

+F3=0.07*P3^2+16*P3+900;//Rs./hr

+C=F1+F2+F3;//Rs/hour

+disp(C,"For this schedule, total cost per hour(Rs./hour)");