Python数学建模PuLP库线性规划入门示例详解

max		fx = 2*x1 + 3*x2 - 5*x3
s.t.	x1 + 3*x2 + x3 <= 12
		2*x1 - 5*x2 + x3 >= 10
		x1 + x2 + x3 = 7
		x1, x2, x3 >=0

    import pulp

    MyProbLP = pulp.LpProblem("LPProbDemo1", sense=pulp.LpMaximize)

    x1 = pulp.LpVariable('x1', lowBound=0, upBound=7, cat='Continuous') 
    x2 = pulp.LpVariable('x2', lowBound=0, upBound=7, cat='Continuous')
    x3 = pulp.LpVariable('x3', lowBound=0, upBound=7, cat='Continuous') 

    MyProbLP += 2*x1 + 3*x2 - 5*x3  	# 设置目标函数

    MyProbLP += (2*x1 - 5*x2 + x3 >= 10)  # 不等式约束
    MyProbLP += (x1 + 3*x2 + x3 <= 12)  # 不等式约束
    MyProbLP += (x1 + x2 + x3 == 7)  # 等式约束

    MyProbLP.solve()
    print("Status:", pulp.LpStatus[MyProbLP.status]) # 输出求解状态
    for v in MyProbLP.variables():
        print(v.name, "=", v.varValue)  # 输出每个变量的最优值
    print("F(x) = ", pulp.value(MyProbLP.objective))  #输出最优解的目标函数值    

import pulp
MyProbLP = pulp.LpProblem("LPProbDemo1", sense=pulp.LpMaximize)
x1 = pulp.LpVariable('x1', lowBound=0, upBound=7, cat='Continuous') 
x2 = pulp.LpVariable('x2', lowBound=0, upBound=7, cat='Continuous') 
x3 = pulp.LpVariable('x3', lowBound=0, upBound=7, cat='Continuous') 
MyProbLP += 2*x1 + 3*x2 - 5*x3  	# 设置目标函数
MyProbLP += (2*x1 - 5*x2 + x3 >= 10)  # 不等式约束
MyProbLP += (x1 + 3*x2 + x3 <= 12)  # 不等式约束
MyProbLP += (x1 + x2 + x3 == 7)  # 等式约束
MyProbLP.solve()
print("Status:", pulp.LpStatus[MyProbLP.status]) # 输出求解状态
for v in MyProbLP.variables():
    print(v.name, "=", v.varValue)  # 输出每个变量的最优值
print("F(x) = ", pulp.value(MyProbLP.objective))  #输出最优解的目标函数值
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Welcome to the CBC MILP Solver 
Version: 2.9.0 
Build Date: Feb 12 2015 
Status: Optimal
x1 = 6.4285714
x2 = 0.57142857
x3 = 0.0
F(x) =  14.57142851