# Add required packages
Pkg.update()
Pkg.add("Optim")
Pkg.add("JuMP")
Pkg.add("Cbc") # for LP and MILP (mixed-integer linear program)
Pkg.add("Ipopt") # for QP and other NLPs
#Pkg.add("Clp")
#Pkg.add("SCS") # for conic programs
#Pkg.add("Gurobi") # for conic and integer programs (commercial license required)
# Pkg.add("CPLEX") # for conic and integer programs (commercial)

# Fractional Shop

using JuMP
using Cbc
#using Gurobi # for LP and MILP

snack = Model(solver=CbcSolver())
#snack = Model(solver=GurobiSolver())

@variable(snack, b >= 0)
@variable(snack, c >= 0)

@objective(snack, Min, 50b + 80c)

@constraints(snack, begin
    3b >= 6
    2b + 4c >= 10
    2b + 5c >= 8
    end)

status = solve(snack)

b = getvalue(b)
c = getvalue(c)
cost = getobjectivevalue(snack)

println("Solver status = $(status)")
println("Brownie $(b), Cheesecake $(c): Total cost $(cost) cents")

# Integer Shop

using JuMP
using Cbc
#using Gurobi # for LP and MILP

snack = Model(solver=CbcSolver())
#snack = Model(solver=GurobiSolver()) # this gives an exactly integral solution

@variable(snack, b >= 0, Int)
@variable(snack, c >= 0, Int)

@objective(snack, Min, 50b + 80c)

@constraints(snack, begin
    3b >= 6
    2b + 4c >= 10
    2b + 5c >= 8
    end)

status = solve(snack)

b = getvalue(b)
c = getvalue(c)
cost = getobjectivevalue(snack)

println("Solver status = $(status)")
println("Brownie $(b), Cheesecake $(c): Total cost $(cost) cents")