import gurobipy as gp
from gurobipy import GRB

def solve_lp():
    # 1. Create model
    model = gp.Model("my_lp")

    # 2. Add variables
    # Example: x, y >= 0
    l = model.addVar(lb=0, ub= 100, name="l", vtype=GRB.CONTINUOUS)
    b = model.addVar(lb=0, ub= 100, name="b", vtype=GRB.INTEGER)
    w = {}
    c = {}
    for i in range(1, 4):
        w[i] = model.addVar(lb=1, ub=1000, name=f"w{i}", vtype= GRB.INTEGER)
    for i in range(1, 4):
        c[i] = model.addVar(lb=1, ub=1000, name=f"c{i}", vtype= GRB.INTEGER)
    ans = model.addVar(lb=0, name="ans", vtype=GRB.CONTINUOUS)

    # 3. Set objective
    # model.setObjective(ans, GRB.MAXIMIZE)
    model.setObjective(l*(c[1]-c[2])-w[2]+w[1], GRB.MAXIMIZE)

    # 4. Add constraints
    # model.addConstr(w[2] >= w[1] >= w[3] >= 0)
    model.addConstr(w[2] >= 0.1+ w[1], name="w2_ge_w1")
    model.addConstr(w[1] >= 0.1+ w[3], name="w1_ge_w3")
    model.addConstr(w[3] >= 0.1+ 0,     name="w3_ge_0")
    # model.addConstr(c[3] >= b >= c[1] >= c[2] >= 0)
    model.addConstr(c[3] >= 0.1+ b,     name="c3_ge_b")
    model.addConstr(b    >= 0.1+ c[1],  name="b_ge_c1")
    model.addConstr(c[1] >= 0.1+ c[2],  name="c1_ge_c2")
    model.addConstr(c[2] >= 0.1+ 0,     name="c2_ge_0")
    model.addConstr((c[3]-c[2])*l >= w[2]-w[3])
    model.addConstr((c[3]-c[2])*l <= w[2]-w[3])
    # model.addConstr(ans*b <= l*(c[1]-c[2])-w[2]+w[1])

    # 5. Optimize
    model.optimize()

    # 6. Retrieve results
    if model.status == GRB.OPTIMAL:
        model.write("gap.json")
    else:
        print("No optimal solution found.")

if __name__ == "__main__":
    solve_lp()