Solve equations with constraints

Can you help me solve equation f with the different constraints established?

I can't get the optimal solution:

syms A k q c k;

beta= sym('beta');

q=(A+beta*k)/3;

c=(A+beta*k)/3;

k=(2*A*beta)/(9-2*beta^2);

f= A*q+beta*q*k-q^2-c*q- k^2/2;

solve(f)

if f>=0

if c>=0

if q>=0

if beta >0

if beta-1<=0

if A>0

end

end

end

end

end

end ;

King regards

Answer 1

[Prabhan Purwar]

Hi,

Following code represents the working of solve and assume functions to solve equations with conditions.

syms A k q c beta; 
  
q=(A+beta*k)/3; 
c=(A+beta*k)/3; 
k=(2*A*beta)/(9-2*beta^2);  
f= A*q+beta*q*k-q^2-c*q- k^2/2; 
  
%Conditions 
%assume(S >= 0); 
assume(c >= 0); 
assume(q >= 0); 
assume(beta > 0); 
assume(beta <= 1); 
assume(A > 0); 
  
%Solve for beta 
S=solve(f,beta,'ReturnConditions',true); 
  
%disply solution 
S  
  
%beta represents required value in terms of parameters 
%parameters are internal variable created to represent multiple solutions 
%conditions represents the assumed conditions imposed upon equation 

Please refer the following link for further information

https://www.mathworks.com/help/symbolic/solve.html

[Zongo Amara Mohamed Isaac]

Thank you so much. It works well