using JuMP

# data.jl has our preference matrix, P
include("data.jl");

# Define the model
m = <WRITE YOUR CODE HERE>

# Define the variables
<WRITE YOUR CODE HERE>

# We want every student to be assigned to exactly one section. 
# So, every row must have exactly one non-zero entry
# In other words, the sum of all the columns for every row is 1
# We also want each section to have between 6 and 10 students, 
# so the sum of all the rows for every column should be between these

# Specify the constraints 
# HINT: you can do it with for-loops of
# the other way I mentioned in class ;)
<WRITE YOUR CODE HERE>


# Our objective is simple sum(X .* P), which can be 
# more efficiently represented as vec(X)' * vec(P)
# Since each entry of X is either 0 or 1, 
# this is basically summing up the rankings of students 
# that were assigned to them.
# If all students got their first choice, 
# this value will be the number of students since 
# the ranking of the first choice is 1.

# Specify the objective
<WRITE YOUR CODE HERE>

# Solve it
@time status = solve(m)
println("Objective value: ", getObjectiveValue(m))
# print the value
# should also be 65.0 ...