How can I optimize two variables with fmincon?

Aim is to minimize variable Z with optimizing S and N. There are two separable files, fieldmodel.m and opt_fieldmodel.m. Running the opt_fieldmodel gives error "Not enough input arguments. Error in fieldmodel (line 28) n(t+1) = n(t)-0.00384*n(t)+0.0243* N(t)-0.000677*Y(t)+0.368*deposit;" How to solve the error and the optimization problem with 2 variables?

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function [Z] = fieldmodel(X,N); 
% parameters
per = 100;      %years
a = 3.5;        %Price of phosphorus, €/kg
b = 1.2;        %Price of nitrogen, €/kg
p = 0.12;       %Price of wheat, €/kg
r = 0.05;       %Interest rate
g = 0;          %Inclination
d = 0;          %Marginal damage
deposit = 4.46;  %deposit
%Variables
Y = zeros(1,per);       %Wheat yield
S = zeros(1,per);       %Soil test phosphorus
n = zeros(1,per);       %Soil test nitrogen
Profit = zeros(1,per);  %Annual profit (€/kg/a)
%Initial state
S(1,1) = 10;
n(1,1) = 200;
 
%Loop
for t=1:per
    Y(t) =  max(0, 837.2 + 73*S(t) + 47.12*n(t) + -2.413*S(t)^2 + 0.0127*S(t)*n(t) + -0.1813*n(t)^2);
    S(t+1) = 0.9816*S(t) + (0.0032+0.00084*S(t))*(X(t)-(3+0.19*log(S(t))*Y(t)/1000));
    n(t+1) = n(t)-0.00384*n(t)+0.0243* N(t)-0.000677*Y(t)+0.368*deposit;
    D(t) = 15*exp(-0.7+0.7*(0.6*X(t)+0.4*N(t))/100);
end
%Profit and NPV
damage = D*70;
Profit = p*Y-a*X - b*N- damage;
Z = - exp(-r*(1:1:per))* Profit;
end

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opt_fieldmodel.m

clear all
X0 = 10*ones(1,100);        %Initial guess for phosphorus
N0 = 10*ones(1,100);        %Initial guess for nitrogen
LB = zeros(1,100);          %Lower bound
UB = 100*ones(1,100);       %Upper bound
 
options = optimoptions(@fmincon,'MaxFunEvals',100000,'Display','iter','MaxIter',8000);
[X,N,FVAL,EXITFLAG] = fmincon(@fieldmodel,[X0,N0],[],[],[],[],LB,UB,[],options)

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Answer 1

[Ameer Hamza]

fmincon accepts a function handle with only one input. I have made few modifications to your code and marked those locations. Compare it with your code to see the difference

% clear all
X0 = 10*ones(1,100);        %Initial guess for phosphorus
N0 = 10*ones(1,100);        %Initial guess for nitrogen
LB = zeros(1,200);          %Lower bound <<===== 200 variables
UB = 100*ones(1,200);       %Upper bound <<===== 200 variables
 
options = optimoptions(@fmincon,'MaxFunEvals',100000,'Display','iter','MaxIter',8000);
[X_sol,FVAL,EXITFLAG] = fmincon(@(x) fieldmodel(x(1:100),x(101:200)),[X0,N0],[],[],[],[],LB,UB,[],options)
X = X_sol(1:100);
N = X_sol(101:200);

function [Z] = fieldmodel(X,N)
% parameters
per = 100;      %years
a = 3.5;        %Price of phosphorus, €/kg
b = 1.2;        %Price of nitrogen, €/kg
p = 0.12;       %Price of wheat, €/kg
r = 0.05;       %Interest rate
g = 0;          %Inclination
d = 0;          %Marginal damage
deposit = 4.46;  %deposit
%Variables
Y = zeros(1,per);       %Wheat yield
S = zeros(1,per);       %Soil test phosphorus
n = zeros(1,per);       %Soil test nitrogen
Profit = zeros(1,per);  %Annual profit (€/kg/a)
%Initial state
S(1,1) = 10;
n(1,1) = 200;
 
%Loop
for t=1:per
    Y(t) =  max(0, 837.2 + 73*S(t) + 47.12*n(t) + -2.413*S(t)^2 + 0.0127*S(t)*n(t) + -0.1813*n(t)^2);
    S(t+1) = 0.9816*S(t) + (0.0032+0.00084*S(t))*(X(t)-(3+0.19*log(S(t))*Y(t)/1000));
    n(t+1) = n(t)-0.00384*n(t)+0.0243* N(t)-0.000677*Y(t)+0.368*deposit;
    D(t) = 15*exp(-0.7+0.7*(0.6*X(t)+0.4*N(t))/100);
end
%Profit and NPV
damage = D*70;
Profit = p*Y-a*X - b*N- damage;
Z = norm(- exp(-r*(1:1:per)).*Profit); % <==== It should return a scalar value, not a vector
end