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

# Specify the variables
# HINT: check what size P has ;)
X = <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 on one line, but it's also
# okay to do it on multiple lines.
# if you wish to add a constraint later on 
# you can do so by:
# constraints += ...
constraints = <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.
p = <WRITE YOUR CODE HERE>

# I specified the solver for you :)
@time solve!(p, GLPKSolverMIP())
p.optval
# correct answer is 65.0 ...