Python cvxpy 库解决 运筹学中的背包问题、目标规划、

Matlab's "linprog" function and Python CVXPY library offer optimal solutions for production.
It can calculate how to achieve maximum profit with limited resources, constraints, and requirements, or simulate the lowest-cost solution.
动态规划中的背包问题：
某工厂生产3种不同的产品，各产品重量与利润关系

    x1 = cp.Variable(integer=True)
    x2 = cp.Variable(integer=True)
    x3 = cp.Variable(integer=True)
    objective = cp.Maximize(80 * x1 + 130 * x2 + 180 * x3)
    constraints = [
        2 * x1 + 3 * x2 + 4 * x3 <= 6,
        x1 >= 0,
        x2 >= 0,
        x3 >= 0,

    ]
    prob = cp.Problem(objective, constraints)
    optimal_value = prob.solve()
    print("最大利润" + str(optimal_value))
    print("产品A:" + str(x1.value))
    print("产品B:" + str(x2.value))
    print("产品C:" + str(x3.value))

题目1：https://blog.csdn.net/clear_lantern/article/details/127622092

import cvxpy as cp

def print_hi(name):
    x1 = cp.Variable()
    x2 = cp.Variable()
    x3 = cp.Variable()
    x4 = cp.Variable()
    objective = cp.Maximize(375 * x1 + 275 * x2 + 475 * x3 + 325 * x4)
    constraints = [
        2.5 * x1 + 1.5 * x2 + 2.75 * x3 + 2 * x4 <= 640,
        3.5 * x1 + 3 * x2 + 3 * x3 + 2 * x4 <= 960,
        x1 >= 0,
        x2 >= 0,
        x3 >= 0,
        x4 >= 0
    ]
    prob = cp.Problem(objective, constraints)
    optimal_value = prob.solve()
    print("最大利润" + str(optimal_value))
    print("产品A:" + str(x1.value))
    print("产品B:" + str(x2.value))
    print("产品C:" + str(x3.value))
    print("产品D:" + str(x4.value))

题目2: https://blog.csdn.net/weixin_43838785/article/details/106335542

import cvxpy as cp

def print_hi(name):
x1 = cp.Variable()
x2 = cp.Variable()
x3 = cp.Variable()

objective = cp.Maximize(3 * x1 + 5 * x2 + 4 * x3)
constraints = [
    2 * x1 + 3 * x2 <= 1500,
    0 * x1 + 2 * x2 + 4 * x3 <= 800,
    3 * x1 + 2 * x2 + 5 * x3 <= 2000,
    x1 >= 0,
    x2 >= 0,
    x3 >= 0,

]
prob = cp.Problem(objective, constraints)
optimal_value = prob.solve()
print("最大利润" + str(optimal_value))
print("产品A:" + str(x1.value))
print("产品B:" + str(x2.value))
print("产品C:" + str(x3.value))

import cvxpy as cp

def print_hi(name):
    x1 = cp.Variable()
    x2 = cp.Variable()
    x3 = cp.Variable()

    objective = cp.Minimize(2 * x1 + 3 * x2 + 1 * x3)
    constraints = [
        x1 + 4 * x2 + 2 * x3 >= 8,
        3 * x1 + 2 * x2 >= 6,
        x1 >= 0,
        x2 >= 0,
        x3 >= 0,

    ]
    prob = cp.Problem(objective, constraints)
    optimal_value = prob.solve()
    print("最小消耗" + str(optimal_value))
    print("产品A:" + str(x1.value))
    print("产品B:" + str(x2.value))
    print("产品C:" + str(x3.value))

import cvxpy as cp

def print_hi(name):
    x1 = cp.Variable()
    x2 = cp.Variable()


    objective = cp.Maximize(2 * x1 + 3 * x2)
    constraints = [
        3 * x1 + 6 * x2 <= 24,
        2 * x1 + 1 * x2 <= 10,
        x1 >= 0,
        x2 >= 0,


    ]
    prob = cp.Problem(objective, constraints)
    optimal_value = prob.solve()
    print("最大利润" + str(optimal_value))
    print("产品A:" + str(x1.value))
    print("产品B:" + str(x2.value))

题目3:https://www.doc88.com/p-9962714762805.html

import cvxpy as cp

def print_hi(name):
    x1 = cp.Variable()
    x2 = cp.Variable()


    objective = cp.Maximize(2 * x1 + 3 * x2)
    constraints = [
        3 * x1 + 6 * x2 <= 24,
        2 * x1 + 1 * x2 <= 10,
        x1 >= 0,
        x2 >= 0,


    ]
    prob = cp.Problem(objective, constraints)
    optimal_value = prob.solve()
    print("最大利润" + str(optimal_value))
    print("产品A:" + str(x1.value))
    print("产品B:" + str(x2.value))

题目4:https://qb.zuoyebang.com/xfe-question/question/5883e50dd60a35e161a23c43eb3c23b8.html

import cvxpy as cp

def print_hi(name):
    x1 = cp.Variable()
    x2 = cp.Variable()

    objective = cp.Maximize(4 * x1 + 3 * x2)
    constraints = [
        2 * x1 + x2 <= 10,
        x1 + x2 <= 8,
        x2 <= 7,
        x1 >= 0,
        x2 >= 0,
    ]
    prob = cp.Problem(objective, constraints)
    optimal_value = prob.solve()
    print("最大利润" + str(optimal_value))
    print("产品A:" + str(x1.value))
    print("产品B:" + str(x2.value))