# Question:maximize a nonlinear objective function

## Question:maximize a nonlinear objective function

Maple

I tried to maximize a nonlinear objective function by mapple 10 but I was not able to obtain non negative solutions. Procedure followed by me is as follows

F:=(-ln(1-s1*(a+beta)/(K-alpha))+ln(1+s1*(a+beta)/(alpha)))/(a+beta)+(-ln(1-s2*beta/alpha)+ln(1+s2*beta/(K-alpha)))/beta;

si:=K*(-(ln(1-s1*(a+beta)/(K-alpha)))/(a+beta)+ln(1+s2*beta/(K-alpha))/beta):

G:=-(-(K-alpha)*ln(1-s1*(a+beta)/(K-alpha))+alpha*ln(1+s1*(a+beta)/(alpha)))/(a+beta)^2:

theta:=-a*(-(K-alpha)*ln(1-s1*(a+beta)/(K-alpha))+alpha*ln(1+s1*(a+beta)/(alpha)))/(a+beta)^2:

phi:=-(alpha*ln(1-s2*beta/alpha)+(K-alpha)*ln(1+s2*beta/(K-alpha)))/beta^2:

Z:=((s-p)*si-C1*G-C3-C2*phi-s*theta)/F:

Zds1:=diff(Z,s1):

Zds2:=diff(Z,s2):

X1:=subs(K=250,alpha=100,p=8,C1=1.5,C2=6,C3=100,a=0.2,beta=0.3,s=10,Zds1):

X2:=subs(K=250,alpha=100,p=8,C1=1.5,C2=6,C3=100,a=0.2,beta=0.3,s=10,Zds2):

X3:=fsolve({X1,X2},{s1,s2});

I got negative values of s1 and s2. Again I tried to maximize the function . The sheet kept on executing but did not gave any result.

X4:=subs(K=250,alpha=100,p=8,C1=1.5,C2=6,C3=100,a=0.2,beta=0.3,s=10,Z):

X5:=maximize(X4,(s1,s2),assumenonnegative);

Hoping to get some response

Regards

Priyasha

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