Optimization of the given set of equation

How to optimize the equation with following constraints

Here our objective function is

where the ranges of ,

Further set of constraints are

1. 
2. 
3. 

and

1. , for and for
2. , for all n

condition of c are

1. when
2. when
3. when

Answer 1

[Nipun]

Hi Sudhir,

I understand that you are trying to optimize the given equation with the specified constraints.

Here is the MATLAB code to solve this optimization problem:

% Define the ranges for B and V
B = 1:1:5;
V = 3.5:0.01:5;

% Pre-allocate the matrix to store results
results = zeros(length(B), length(V));

% Iterate over each combination of B and V
for i = 1:length(B)
    for j = 1:length(V)
        b = B(i);
        v = V(j);

        % Define tc based on the given constraints
        n = 4; % Example value of n, can be varied as needed
        if n < 3
            f2 = 0;
        else
            if n > 3
                c = 2; % Example value, vary as per conditions
                if n >= 6 && n <= 10
                    c = 3;
                elseif n > 10 && n <= 15
                    c = 4;
                end
                f2 = 4042.5 * c / (n - 3);
            else
                f2 = 0;
            end
        end
        f1 = 404250 / n;
        v1 = 6240 * v * b;
        v2 = 1803.3 * b;
        tc = v1 + v2 + f1 + f2;

        % Calculate the objective function
        Cop = tc / (280.8 * v * b);

        % Store the result
        results(i, j) = Cop;
    end
end

% Find the minimum value of the objective function and its indices
[minCop, idx] = min(results(:));
[row, col] = ind2sub(size(results), idx);

% Get the optimal B and V values
optimalB = B(row);
optimalV = V(col);

% Display the results
fprintf('The minimum value of Cop is: %.4f\n', minCop);
fprintf('This occurs at B = %.2f and V = %.2f\n', optimalB, optimalV);

This code iterates over all combinations of 𝐵 and 𝑉, computes the objective function 𝐶𝑜𝑝 for each combination while considering the constraints, and finds the optimal values that minimize 𝐶𝑜𝑝. Adjust the value of 𝑛 as needed based on the specific scenario.

Hope this helps.

Regards,

Nipun