How to optimise taxes

Hi everyone

I have working on a code which would allow me to look the optimal level of taxes the goverment could apply, so I have created both demand and supply functions and I have used fmincon but I do not know how can set Government tax= T*Q.

Should I create another function?

This is what I have so far:

function [x, fval, expected_return] = effportfolio(fun, Sigma, mu, mu_p_0, initial_guess, optimisation_options)

%EFFPORTFOLIO solves for the efficient portfolio

%optimisation_options

if nargin<6

optimisation_options=[];

end

%% constraints

Aeq = [mu' ; ones(1,length(mu))];

beq = [mu_p_0;1];

%% Minimisation

if strcmp(fun, 'quadprog')

[x, fval] = quadprog(Sigma, [], [], [], Aeq, beq) ;

else

[x, fval] = fmincon(@effportobj, initial_guess, [], [], Aeq, beq, [], [], [], optimisation_options, Sigma) ;

end

expected_return = x'*mu;

end

function z = effportobj(x, Sigma)

z = x'*Sigma*x;

end

function fun = myfun2

fun{1} = @(P) 1*Q+10+T;

fun{2} = @(P) -3*Q+90;

end

Thank you very much

[Joao Pereira]

I have also find this example which I think it may be

https://l.facebook.com/l.php?u=https%3A%2F%2Fwww.mathworks.com%2Fhelp%2Foptim%2Fug%2Fexample-nonlinear-constrained-minimization.html%3Ffbclid%3DIwAR0yYyblrh29WZ9HcUwnH0l68qsyp5rF1fRAiZcBtDW4eVd2t0TTrGytOuo&h=AT249AnzXCK9gaJYHhNeD0A2_3uTNILsHWjcjuog7SpK5EO9HUjSFH38YFT0s6H40pg3c395KjFsTH57folQs_Mgbq0UFMBkyJOkbMA433GUG-bW0nFNRxtWv1Lv9d-PKJcXDg