MATLAB: Solve equations with constraints

equationsolve

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

Best Answer

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
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