py1

import pulp

# 定义问题
model = pulp.LpProblem("Player_Salaries_Optimization", pulp.LpMinimize)

# 定义决策变量
x12 = pulp.LpVariable("x12", lowBound=0, cat='Integer')
x23 = pulp.LpVariable("x23", lowBound=0, cat='Integer')
x34 = pulp.LpVariable("x34", lowBound=0, cat='Integer')
x45 = pulp.LpVariable("x45", lowBound=0, cat='Integer')
y1 = pulp.LpVariable("y1", lowBound=0, upBound=2, cat='Integer')
y2 = pulp.LpVariable("y2", lowBound=0, upBound=4, cat='Integer')
y3 = pulp.LpVariable("y3", lowBound=0, upBound=10, cat='Integer')
y4 = pulp.LpVariable("y4", lowBound=0, upBound=12, cat='Integer')
y5 = pulp.LpVariable("y5", lowBound=0, upBound=260, cat='Integer')
z = pulp.LpVariable("z", lowBound=0, cat='Integer')
w = pulp.LpVariable("w", lowBound=0, cat='Integer')
# 此处引入辅助变量w来平衡薪资总额的约束和III和IV级球员的人数最大化这两个目标
# 并在目标函数中加入了一个很大的系数（例如1000000），以确保y3+y4的值尽可能大。

# 目标函数
model += 2000 * x12 + 1500 * x23 + 1000 * x34 + 300 * x45 + 2000 * y1 + 1500 * y2 + 1000 * y3 + 300 * y4 + 10 * y5 + 10 * z + 1000000 * (y3 + y4 - w)


# 约束条件
model += y1 + y2 + y3 + y4 + y5 + z == 253, "Total_Players"
model += 2000 * x12 + 1500 * x23 + 1000 * x34 + 300 * x45 + 2000 * y1 + 1500 * y2 + 1000 * y3 + 300 * y4 + 10 * y5 + 10 * z <= 23000, "Salary_Cap"
model += x12 <= y1, "Promotion_Constraint_1"
model += x23 <= y2, "Promotion_Constraint_2"
model += x34 <= y3, "Promotion_Constraint_3"
model += x45 <= y4, "Promotion_Constraint_4"
model += y3 + y4 == w, "Balance_Objective"

# 求解问题
model.solve()

# 输出结果
print("Status:", pulp.LpStatus[model.status])
for var in model.variables():
    print(f"{var.name}: {var.varValue}")
print("Total Salary:", pulp.value(model.objective))