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syms P M r
%Parameters
W=21; C=10; a=500; b=10; Ss=40; Sr=20; hrs=3; Ir=0.13; Is=0.1;
A=800; K=3;

P1 = hrs+W*Ir;
P2 = r*b*W*Ir/C/Is; % LM: -(a-bP)CIs+rbWIr = 0

LP=-b*(W-C)+b*Ss*sqrt(P1/72/Sr/P2)+b*hrs*(2-P2/A)*sqrt(Sr/8/P1/P2)-...
    hrs*b/A*sqrt(P2*Sr/2/P1)+b*M*C*Is-r*(-2*b+b^2/4/P2^2)*sqrt(2*Sr*P1*P2);

Constraint = r*b*W*Ir/C/Is*2-a+b*W-b*M*W*Ir+b*sqrt(Sr*P1/2/P2);
f = subs(LP,'M',solve(Constraint,M));
rvalue = solve(f);
Pvalue = a/b-rvalue*W*Ir/C/Is

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