please, I want someone to help me with MATLAB code for solving the non linear constrained equation as given below

Objective function Max f= 5/3 x_1^(3/44) x_2^(4/7) x_3^(3/40) x_4^(2/9) x_5^(1/6)

Constraints

17x_1+20x_2+10x_3+0.4x_4+1.5x_5≤240

x_4 ≤ 30

x_5≤ 100

[John D'Errico]

Please don't add an answer just to make a comment.

Answer 1

[William Rose]

@Ezra Dzarma,

[edit: added lines to display -f(x) and constraint 1 at the solution point.]

Please carefully read the help for fmincon(). The name is short for "function minimization with constraints". Minimize the negative of your function. fmincon() can do exactly what you want, including the constraints. The examples in the help doc will be useful.

%vector x is what you want to find
fun = @(x)-5/3*x(1)^(3/44)*x(2)^(4/7)*x(3)^(3/40)*x(4)^(2/9)*x(5)^(1/6);
x0=[1,1,1,1,1];  %initial guess for the solution
%express first constraint in the form A*x<=b:
A=[17,20,10,0.4,1.5]; b=240;
%express constraints 2 and 3 by defining vectors lb and ub:
lb=[-Inf,-Inf,-Inf,-Inf,-Inf];  %no lower blound constraints
ub=[Inf,Inf,Inf,30,100];  %upper bounds on x(4),x(5)
x=fmincon(fun,x0,A,b,[],[],lb,ub);

Local minimum found that satisfies the constraints.

Optimization completed because the objective function is non-decreasing in 
feasible directions, to within the value of the optimality tolerance,
and constraints are satisfied to within the value of the constraint tolerance.

disp(x)         %value of x at the solution

    1.0376    7.3919    1.9404   30.0000   28.7462

disp(-fun(x));  %value of the function you wanted to maximize

   20.5263

disp(A*x')      %check constraint 1

  240.0000

Note that constraint 1 is met exactly, constraint 2 is met exactly, and constraint 3 is not approached. Good luck.

[William Rose]

@Ezra Dzarma, you are welcome. If my answer meets your needs, then please accept it.

[John D'Errico]

Please don't do obvious homework assignments for students. It does not help the student, because they learn nothing except that there will be someone to take pity on them and do their work for them.

[Ezra Dzarma]

Please, the question posted is a research question, I have been looking for a solution for a long time, I think there is nothing wrong in the response of prof Rose. Please, sorry in case you are offended Thank

[William Rose]

@John D'Errico, Thank you for that advice.