using JuMP
using GLPKMathProgInterface
m = Model(solver = GLPKSolverMIP())

demand = [12,14,16,18,20,22,24,26,28,30]
probs = [0.05,0.1,0.1,0.1,0.15,0.15,0.1,0.1,0.1,0.05]
buy = 21

@variable(m,x >= 0, Int)
@variable(m,y[1:10] >= 0, Int)
@variable(m,w[1:10] >= 0,Int)

@objective(m, Max, sum(probs[i]*(50*w[i] - 10*y[i]) for i=1:10) )

@constraint(m, loop[i=1:10] , w[i] <= x)
@constraint(m, loop[i=1:10] , w[i] <= demand[i])

@constraint(m, loop[i=1:10], y[i] == x - w[i])

solution = solve(m)
print(m)
println("Objective value: ",getobjectivevalue(m))


demand = [12,14,16,18,20,22,24,26,28,30]
probs = [0.05,0.1,0.1,0.1,0.15,0.15,0.1,0.1,0.1,0.05]
buy = 21

total = sum(probs[i]*(50*min(demand[i],buy)-10*max(buy-demand[i],0)) for i=1:10)
println(total)

total2 = sum(probs[i]*50*demand[i] for i=1:10)

println(total2)