Binary integer programming using bintprog in Matlab

bintprog_grades.m

clear all; clc; home;

%{
f = -[1 1.3 1.7 2];

A = [1 1 1 1;           % sum of all parameters
     1 1.3 1.7 2]       % weight of all parameters

 b = [1;                % sum of all parameters not larger than 1
     1.5];              % the target grade

x = bintprog(f, A, b)
%}

% your already known grades
have = [1 1 1.3 1];

% the number of exams still to write
N = 9;

% your worst-case mean grade
worst_case = 1.49;

% the grades you expect to write
grades = [1 1.3 1.7  2 2.3 2.7   3];

% build the objective function
n = repmat(grades, 1, N);
g = [have n];
f = -g;

% constraints: mean grade
M = N + length(have);
A = g * (1/M);
b = worst_case;

% constraints: number of grades selected
Aeq = [[ones(size(have)) zeros(size(n))];  % all the known graded
       [zeros(size(have)) ones(size(n))]]; % all but the known grades
beq = [length(have); 
       N];

% solve the problem -- may take ages
x = bintprog(f, A, b, Aeq, beq);

% select solutions from objective function
grades = g(x ~= 0);

% remove known grades without duplicates
while ~isempty(have)
    grades(find(grades == have(1), 1, 'first')) = [];
    have(1) = [];
end

% print your worst-case scenario grades
there_you_go = sort(grades, 'descend')