I want to solve the unknown variable t1

I want to solve t1 from the equation S1 and then apply value of t1 in TC. But I couldn't find t1. I don't know where I left the mistake.

clc

clear all

A0 =500;

D0=100;

c1=5;

c2=10;

c3=10;

c4=8;

a=30;

a2=40;

m=0.5;

b=5;

b2=7;

mu1=4;

mu2=8;

T=12;

k1=0.01;

k0=0.03;

syms t1

S1='(1./T).*(c1.*((b-a)-b.*t1-((a+b.*(1+m))./(1+m-t1)))+c2.*(b.*t1-((a+b.*(1+m).*t1)./(1+m-t1)))+c3.*((a./k1)-(b.*(1-k1.*T)./k1^2).*(((-mu1.*k1)./(1+k1.*(t1-T)))+1)-((1-k1.*T)./(1+k1.*(t1-T)))+((b.*k0.*(t1-mu1))./k1)-((a-b.*k0.*(1-k1.*T))./k1).*((mu2-mu1)./(1+k1.*(t1-T)))+(k0.*D0./k1).*((k1.*(mu1-mu2)./(1+k1.*(t1-T)))-(a-((b.*k0.*(1-k1.*T))./k1)).*((T-k2)./(1+k1.*(t1-T)))+(b.*k0.*(mu2-T)./k1)-(1-k1.*T).*((T+mu2)./(1+k1.*(t1-T)))))+c4.*(-a2+b2.*t1+k0.*((a-b.*(1-k1.*T))./k1).*(1./(1+k1.*(t1-T)))+(b./k1)))';

t1=solve'S1'

TC=(1./T).*(A0+c1.*((b-a).*t1-(b.*t1^2./2)+(a+b.*(1+m)).*log((1+m-t1)./(1+m)))+c2.*((b.*t1^2./2)+(a+b.*(1+m)).*(t1+(1+m).*log(1+m-t1)))+c3.*((a./k1)-(b.*(1-k1.*T)./k1^2).*(mu1.*(log((1+k1.*(mu1-T))./(1+k1.*(t1-T)))-1)+t1)+((1-k1.*T)./k1).*(log((1+k1.*(mu1-T))./(1+k1.*(t1-T))))+(b.*k0./2.*k1).*(mu1-t1).^2+((a./k1)-(b.*k0.*(1-k1.*T)./k1^2).*(log((1+k1.*(mu1-T))./(1+k1.*(t1-T)))).*(mu2-mu1)+(k0.*D0./k1).*(mu2.*(log((1+k1.*(mu2-T))./(1+k1.*(t1-T)))-1)-mu1.*(log((1+k1.*(mu1-T))./(1+k1.*(t1-T)))-1)+((1-k1.*T)./k1).*(log((1+k1.*(mu2-T))./(1+k1.*(mu1-T))))+((a./k1)-(b.*k0.*(1-k1.*T)./k1^2).*(log((1+k1.*(mu1-T))./(1+k1.*(t1-T)))).*(T-mu2)+(b.*k0./k1).*(mu1-t1).*(T-mu2)+(k0.*D0./k1).*(log((1+k1.*(mu2-T))./(1+k1.*(mu1-T)))).*(T-mu2)-(k0.*b2./2.*k1).*(mu2-T).^2+((1./k1)-T)+(T-(1./k1)).*(T.*(log(1+k1(t1-T))-1)-mu2.*(log((1+k1.*(mu2-T))./(1+k1.*(t1-T)))-1))+(T-(1./k1)).*log(1+k1.*(mu2-T))))+c4.*(a.*(mu1-t1)+(b2./2).*(mu1.^2-t1.^2)-k0.*(a./k1)-(b.*(1-k1.*T)./k1^2).*(log((1+k1.*(mu1-T))./(1+k1.*(t1-T))))+(b./k1).*(mu1-t1))+D0.*(mu2-mu1)-(D0.*k0./k1).*(log((1+k1.*(mu2-T))./(1+k1.*(mu1-T))))+(1./2.*b2).*((a2-b2.*mu2).^2-(a2-b2.*T).^2)+k0.*a2.*log(1+k1.*(mu2-T))-(b2./k1).*(T-mu2)+(b2./k1).*(T-(1./k1)).*log(1+k1.*(mu2-T)))));

plot(t,TC)

Answer 1

[Alan Stevens]

Well, this gets it working, though who knows if it makes any sense!"

A0 =500;
D0=100;
c1=5;
c2=10;
c3=10;
c4=8;
a=30;
a2=40;
m=0.5;
b=5;
b2=7;
mu1=4;
mu2=8;
T=12;
k1=0.01;
k0=0.03;

k2 = 0; % Replace with true value

syms t1
S1=(1./T).*(c1.*((b-a)-b.*t1-((a+b.*(1+m))./(1+m-t1)))+c2.*(b.*t1-((a+b.*(1+m).*t1)./(1+m-t1)))+c3.*((a./k1)-(b.*(1-k1.*T)./k1^2).*(((-mu1.*k1)./(1+k1.*(t1-T)))+1)-((1-k1.*T)./(1+k1.*(t1-T)))+((b.*k0.*(t1-mu1))./k1)-((a-b.*k0.*(1-k1.*T))./k1).*((mu2-mu1)./(1+k1.*(t1-T)))+(k0.*D0./k1).*((k1.*(mu1-mu2)./(1+k1.*(t1-T)))-(a-((b.*k0.*(1-k1.*T))./k1)).*((T-k2)./(1+k1.*(t1-T)))+(b.*k0.*(mu2-T)./k1)-(1-k1.*T).*((T+mu2)./(1+k1.*(t1-T)))))+c4.*(-a2+b2.*t1+k0.*((a-b.*(1-k1.*T))./k1).*(1./(1+k1.*(t1-T)))+(b./k1)));
t1=solve(S1,t1);

TC=(1./T).*(A0+c1.*((b-a).*t1-(b.*t1.^2./2)+(a+b.*(1+m)).*log((1+m-t1)./(1+m)))+c2.*((b.*t1.^2./2)+(a+b.*(1+m)).*(t1+(1+m).*log(1+m-t1)))+c3.*((a./k1)-(b.*(1-k1.*T)./k1^2).*(mu1.*(log((1+k1.*(mu1-T))./(1+k1.*(t1-T)))-1)...
    +t1)+((1-k1.*T)./k1).*(log((1+k1.*(mu1-T))./(1+k1.*(t1-T))))...
    +(b.*k0./2.*k1).*(mu1-t1).^2+((a./k1)-(b.*k0.*(1-k1.*T)./k1^2).*(log((1+k1.*(mu1-T))./(1+k1.*(t1-T)))).*(mu2-mu1)+(k0.*D0./k1).*(mu2.*(log((1+k1.*(mu2-T))./(1+k1.*(t1-T)))-1)-mu1.*(log((1+k1.*(mu1-T))./(1+k1.*(t1-T)))-1)...
    +((1-k1.*T)./k1).*(log((1+k1.*(mu2-T))./(1+k1.*(mu1-T))))+((a./k1)...
    -(b.*k0.*(1-k1.*T)./k1^2).*(log((1+k1.*(mu1-T))./(1+k1.*(t1-T)))).*(T-mu2)...
    +(b.*k0./k1).*(mu1-t1).*(T-mu2)+(k0.*D0./k1).*(log((1+k1.*(mu2-T))./(1+k1.*(mu1-T)))).*(T-mu2)-(k0.*b2./2.*k1).*(mu2-T).^2 ...
+((1./k1)-T)+(T-(1./k1)).*(T.*(log(1+k1.*(t1-T))-1) ...
-mu2.*(log((1+k1.*(mu2-T))./(1+k1.*(t1-T)))-1))+(T-(1./k1)).*log(1+k1.*(mu2-T))))...
+c4.*(a.*(mu1-t1)+(b2./2).*(mu1.^2-t1.^2)-k0.*(a./k1)...
-(b.*(1-k1.*T)./k1^2).*(log((1+k1.*(mu1-T))./(1+k1.*(t1-T))))...
+(b./k1).*(mu1-t1))+D0.*(mu2-mu1)-(D0.*k0./k1).*(log((1+k1.*(mu2-T))./(1+k1.*(mu1-T))))...
+(1./2.*b2).*((a2-b2.*mu2).^2-(a2-b2.*T).^2)+k0.*a2.*log(1+k1.*(mu2-T))-(b2./k1).*(T-mu2)+(b2./k1).*(T-(1./k1)).*log(1+k1.*(mu2-T)))));

disp('TC')

TC

disp(TC)

disp(vpa(TC))

disp('t1')

t1

disp(t1)

disp(vpa(t1))

[M.Rameswari Sudha]

Thank you for giving the answer. It is very useful to me.