How can I solve this matrix question using for loop?

Dear all,

There is a problem that I need to solve in the attached picture. First I defined the benefit matrix as A, and then I set up a for loop and tried to find the newly formed benefit matrices in the tables for each user from 1 unit of water to 8 units of water with this code. However, I think I'm making a math error because it's not giving the correct result. I need to calculate the benefits for each user and show the maximum and how many units of water should go to each user as a result. How can I do it?

clc;
clear;
close all;

A=[6 5 7;12 14 30;35 40 42;75 55 50;85 65 60;91 70 70;96 75 72;100 80 75]; %the matrix of benefits for each user

%for 3 users
for i=1:8
    v(i)=A(i,3)
        %for 2 users
        for j=1:8
            v(j)= A(j,2); 
                %for 1 user
                for k=1:8
                    v(k)=A(k,1);
                end
        end
end

Answer 1

[Torsten]

Not the most efficient solution, but maybe best to understand what's happening.

A=[0 0 0 ;6 5 7;12 14 30;35 40 42;75 55 50;85 65 60;91 70 70;96 75 72;100 80 75];
max_benefit = -Inf;
index_user = zeros(1,3);
units_of_water = 8;
for i = 0:units_of_water
    for j = 0:units_of_water
        for k = 0:units_of_water
            if i+j+k <= units_of_water
              benefit = A(i+1,1) + A(j+1,2) + A(k+1,3);
              if benefit > max_benefit
                units_of_water_per_user = [i, j, k];
                max_benefit = benefit;
              end
            end
        end 
    end
end
max_benefit

max_benefit = 130

units_of_water_per_user

units_of_water_per_user = 1×3

4 4 0

[Sena]

thank you for reply. I'll try again with your answer.