使用纸浆进行优化仅给出0作为结果

Question

我正在编写一个代码，该代码在给定一组约束的情况下最大化了我的目标函数的值。它具有四个标记X1至X4的变量，具有两个等式约束和两个不等式约束。使用linprog解决给我适当的结果。但是，使用纸浆方法仅给我零作为结果。

from pulp import LpMaximize, LpProblem, LpStatus, lpSum, LpVariable
import numpy as np

# Create the model
model = LpProblem(name="optimize", sense=LpMaximize)

# Initialize the decision variables
x1 = LpVariable(name="x1", lowBound= 0, upBound = None, cat='Continuous')
x2 = LpVariable(name="x2", lowBound= 0, upBound = 5, cat='Continuous')
x3 = LpVariable(name="x3", lowBound=None, upBound = 0.5, cat='Continuous')
x4 = LpVariable(name="x4", lowBound=-3, upBound = None, cat='Continuous')

#Objective function of the model
obj_func =  (29 * x1 + 45 * x2)
model += obj_func


# Add the constraints to the model
model += (x1 - x2 - 3 * x3 <= 5, "Constraint_1")
model += (2 * x1 - 3 * x2 -7 * x3 + 3 * x4 >= 10, "Constraint_2")
model += (2 * x1 + 8 * x2 + x3 == 60, "Constraint_3")
model += (4 * x1 + 4 * x2 + x4 == 60, "Constraint_4")

model

# Solve the problem
status = model.solve()

LpStatus[model.status]

model.variables()

for var in model.variables():
     print(f"{var.name}: {var.value()}")

我可以看到lpstatus [model.status]在说解决方案是未定义的。

相同的一组方程为我提供了linprog中的解决方案 [6.60059411，3.973669，-0.52664072，1.09008012]

Answer 1

您的解决方案无法满足第二个约束。查看：
2x6.60059411-3x3.973669-7x（-0.52664072） + 3x1.09008012 = 8.2369＆lt; 10