# how to find optimal solutions for the given problem?

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M.Rameswari Sudha on 25 Apr 2024
Edited: Mathieu NOE on 25 Apr 2024
I got the answer. but i want to get optimal answer. I couldnt able to get convex graph for this problem.
function newton2D10()
%New trade credit case 1 T&gt;=t
clc
close all
n=0:1:10;
q=0:100:900;
[q,n]=meshgrid(q,n);
TCTC=f(q,n);
mesh(q,n,TCTC)
r0=[0.20;10];
alfa=0.2;
while abs (f(r0(1),r0(2))) &gt; 1e-2
r0 = r0 - alfa.*(f(r0(1),r0(2)))./fprime(r0(1),r0(2));
end
hold on
r0=[8;0.1]
alfa=0.2;
for index = 1:100
r0 = r0 - alfa.*inv(fdb1prime(r0(1),r0(2))).*fprime(r0(1),r0(2));
end
r0
f(r0(1),r0(2))
plot(r0(1),r0(2),f(r0(1),r0(2)),&#39;rs&#39;,&#39;Markersize&#39;,20)
function TC = f(q,n)
pr=7;
p=2000;
P=1;
Ic=0.15;
t=0.25;
Id=0.05;
%p=1600;
%pmin=700;
%pmax=1200;
%D=1600;
D=1000;
z=4;
m=10;
hr=5;
%h1=12;
%h2=11;
%h3=13;
%hb=19.24;
h1=2;
h2=1;
h3=3;
hb=9;
cL=4;
c=2;
c0=12;
c1=13;
c2=12;
ce=15;
Ct=100;
k=0.5;
%k1=0.05;
k1=70;
alpha=0.01;
beta=0.099;
%u=0.999;
u=0.999;
%s=250;
%A=150;
s=25;
A=15;
g0=5;
g1=2;
theta1=1;
theta2=0.6;
w0=0.3;
w1=0.2;
F=50;
sigma=5;
%ts=0.17;
%pi=80;
ts=0.25;
pi=80;
zeta=0.5;
%zeta1=300;
%zeta2=1/300;
zeta1=300;
zeta2=1/300;
sp=15;
sc=0.5;
pc=3;
Ic=0.15;
t=0.25;
TC=((((2.*A+2.*F+((D.*P.*t^2).*(Ic-
Id)))./2)+(n.*Ct)).*(D./n.*q))+hb.*((q./2)+(k1.*sigma.*sqrt(ts+(q./p)))+(((D.
*pi.*sigma)./(n.*q.*2)).*sqrt(ts+(q./p))).*(sqrt(1+k1^2).*k1))+((zeta+sp).*D)
+ ((n.*q).*((2.*sc+P.*Ic)./2))+(pr.*D)
+(z.*(m.*D./n.*q))+((hr+cL.*k).*(D.*n.*q./2.*m.*p))+(h1.*(1-(((2.*u-
1).*D)./(2.*p.*u))).*n.*q)-
(h1.*n.*q./2)+(s.*D./n.*q)+((D./u).*(c0+(c1.*alpha)+(c0.*alpha)+(c2.*(1-
beta).*alpha)))+((c.*D./n.*q).*(g0+g1.*n.*q))+(((D.*ce.*n.*theta1)./(n.*q)).*
(g0+g1.*n.*q))+((w0+w1.*(((1-(((2.*u-1).*D)./(2.*p.*u))).*n.*q)-
(n.*q./2))).*ce.*theta2)+(D.*zeta1.*p)+(D.*zeta2./p)+((pc.*Ic)./(1+(Ic.*t)))-
( D.*P.*t.*Ic);
function TCprime = fprime(q,n)
dfdq =-((((2*A+2*F+((D*P*t^2)*(Ic-
Id)))/2)+(n*Ct))*(D/n*q^2))+(hb*(1/2+((k1*sigma)/(2*p*sqrt(ts+(q/p))))))-
((D*pi/n*q^2)*((sigma/2)*(sqrt(ts+(q/p))*(sqrt(1+k1^2)-
k1))))+((D*pi/n*q)*((sigma/2*p*sqrt(ts+(q/p))*(sqrt(1+k1^2)-
k1))))+(n*((2*sc+P*Ic)/2))-(z*m*D/n*q^2)+((hr+cL*k)*(D*n/2*m*p))+(h1*(1-
(((2*u-1)*D)/(2*p*u)))*n)-(h1*n/2)-(s*D/n*q^2)-(c*D*g0/n*q^2)-
(D*ce*n*theta1*g0/n*q^2)+(w1*(1-(((2*u-1)*D)/(2*p*u))*n-(n/2))*ce*theta2);
dfdn =-((((2*A+2*F+((D*P*t^2)*(Ic-Id)))/2))*(D/q*n^2))-
((D*pi/q*n^2)*((sigma/2)*(sqrt(ts+(q/p))*(sqrt(1+k1^2)-
k1)))+(q*((2*sc+P*Ic)/2))-(z*m*D/q*n^2)+((hr+cL*k)*(D*q/2*m*p))+(h1*(1-
(((2*u-1)*D)/(2*p*u)))*q)-(h1*q/2)-(s*D/q*n^2)-
(c*D*g0/q*n^2)+D*ce*theta1*g1)+(w1*(1-(((2*u-1)*D)/(2*p*u))*q-
(q/2))*ce*theta2);
TCprime =[dfdq;dfdn]
function TCdb1prime = fdb1prime(q,n)
df2dq2=((((2*A+2*F+((D*P*t^2)*(Ic-
Id)))/2)+n*Ct)*(2*D/n*q^3))+((hb*k1*sigma/2*p)*((ts+(q/p)^(-3/2))))
+((2*D*pi/n*q^3)*((sigma/2)*(sqrt(ts+(q/p))*(sqrt(1+k1^2)-
k1))))+((D*pi/n*q^2)*(sigma/(2*p*sqrt(ts+(q/p))))*(k1-
sqrt(1+k1^2)))+((D*pi/n*q^2)*(sigma/2*p*sqrt(ts+(q/p)))*(k1-
sqrt(1+k1^2)))+((D*pi/n*q)*(sigma/4*p^2)*((ts+(q/p))^(-3/2))*(k1-
sqrt(1+k1^2)))+(2*z*m*D/n*q^3)+(2*s*D/n*q^3)+(2*c*D*g0/n*q^3)+(2*D*ce*theta1*
g0/q^3);
df2dqn=((((2*A+2*F+((D*P*t^2)*(Ic-
Id)))/2))*(2*D/q^2*n^2))+((2*sc+P*Ic)/2)-
((D*pi/n^2*q^2)*((sigma/2)*(sqrt(ts+(q/p))*(sqrt(1+k1^2)-
k1))))+((D*pi/n^2*q)*(( sigma/2*p*sqrt(ts+(q/p))*(sqrt(1+k1^2)-k1))))+sc-
(z*m*D/n^2* q^2)+((hr+cL*k)*(D/2*m*p))+(h1*(1-(((2*u-1)*D)/(2*p*u))))-(h1/2)-
(s*D/n^2*q^2)-(c*D*g0/n^2*q^2)+w1*(1-(((2*u-1)*D)/(2*p*u))-(1/2))*ce*theta2;
df2dnq =((((2*A+2*F+((D*P*t^2)*(Ic-
Id)))/2))*(2*D/q^2*n^2))+((2*sc+P*Ic)/2)-
((D*pi/n^2*q^2)*((sigma/2)*(sqrt(ts+(q/p))*(sqrt(1+k1^2)-
k1))))+((D*pi/n^2*q)*(( sigma/2*p*sqrt(ts+(q/p))*(sqrt(1+k1^2)-k1))))+sc-
(z*m*D/n^2* q^2)+((hr+cL*k)*(D/2*m*p))+(h1*(1-(((2*u-1)*D)/(2*p*u))))-(h1/2)-
(s*D/n^2*q^2)-(c*D*g0/n^2*q^2)+w1*(1-(((2*u-1)*D)/(2*p*u))-(1/2))*ce*theta2;
df2dn2=((((2*A+2*F+((D*P*t^2)*(Ic-Id)))/2))*(2*D/q*n^3))-
((D*pi/n^2*q^2)*((sigma/2)*(sqrt(ts+(q/p))*(sqrt(1+k1^2)-
k1))))+((D*pi/n^2*q)*(( sigma/2*p*sqrt(ts+(q/p))*(sqrt(1+k1^2)-k1))))+sc-
(z*m*D/n^2* q^2)+((hr+cL*k)*(D/2*m*p))+(h1*(1-(((2*u-1)*D)/(2*p*u))))-(h1/2)-
(s*D/n^2*q^2)-(c*D*g0/n^2*q^2)+w1*(1-(((2*u-1)*D)/(2*p*u))-(1/2))*ce*theta2;
end
end
end
end

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