python数学建模算法与应用【吴老师亲启】——第四章习题

4.1

法一：

#程序文件ti4_1_1.py
import cvxpy as cp
x=cp.Variable(2,pos=True)
obj=cp.Maximize(72*x[0]+64*x[1])
con=[x[0]+x[1]<=50, 12*x[0]+8*x[1]<=480, 3*x[0]<=100]
prob=cp.Problem(obj,con)
prob.solve(solver="GLPK_MI")
print("最优值为：",prob.value); print("最优解为：\n",x.value)

最优值为： 3360.0
最优解为：
 [20. 30.] 

 法二：

#程序文件ti4_1_2.py
import cvxpy as cp
import numpy as np
x=cp.Variable(2,pos=True)
c=np.array([72,64])
a=np.array([[1,1],[12,8],[3,0]])
b=np.array([50,480,100])
obj=cp.Maximize(c@x); con=[a@x<=b]
prob=cp.Problem(obj,con)
prob.solve(solver="GLPK_MI")
print("最优值为：",prob.value); print("最优解为：",x.value)

最优值为： 3360.0
最优解为： [20. 30.] 

4.2

#程序文件ti4_2.py
import cvxpy as cp
import numpy as np
x=cp.Variable(5,integer=True)
c=np.array([20,90,80,70,30])
a=np.array([[-1,-1,0,0,-1], [0,0,-1,-1,0], [3,0,2,0,0], [0,3,0,2,1]])
b=np.array([-30,-30,120,48])
prob=cp.Problem(cp.Minimize(c@x), [a@x<=b, x>=0])
prob.solve(solver="GLPK_MI")
print("最优值为：", prob.value); print("最优解为：\n", x.value)

最优值为： 2760.0
最优解为：
 [30.  0.  6. 24.  0.] 

4.3

#程序文件ti4_3.py
import pylab as plt
import numpy as np
import cvxpy as cp
plt.rc('text',usetex=True); plt.rc('font',size=16)
x=cp.Variable(6,pos=True)
obj=cp.Minimize(x[5])
a1=np.array([0.025, 0.015, 0.055, 0.026])
a2=np.array([0.05, 0.27, 0.19, 0.185, 0.185])
a3=np.array([1, 1.01, 1.02, 1.045, 1.065])
k=0.05; kk=[]; ss=[]; X=[]
while k<0.27:
    con=[cp.multiply(a1,x[1:5])<=x[5],
         a2@x[:-1]>=10000*k, a3@x[:-1]==10000]
    prob=cp.Problem(obj,con)
    prob.solve(solver='GLPK_MI')
    kk.append(k); ss.append(prob.value)
    X.append(x.value); k=k+0.005
plt.plot(kk,ss,'r*'); plt.xlabel('$k$')
plt.ylabel('$R$',rotation=0); plt.show()
print(round(ss[32],2)); print(np.round(X[32],2))

 77.22
[   0.   3088.74 5147.9  1403.97  152.45   77.22]

 

4.4

#程序文件ti4_4.py
import cvxpy as cp
import numpy as np
x=cp.Va