human
I am working on the file "SimplexAlgorithm.ipynb".
The first task is:
Given the  following optimization problem
$\hspace{2.7cm} \min c^T\textbf{x}$
subject to $\hspace{.1cm} A_{eq}\textbf{x} = \textbf{b}_{eq}$
$\hspace{2.7cm} A_u \textbf{x} \leq \textbf{b}_u$
$\hspace{3.5cm}  \textbf{x} \geq \textbf{0}$
The simplex algorithm as class object will be initialize with
c: cost vector $c^T$
A: $A_{eq}$
b: $b_{eq}$
A_l: $A_{u}$
b_l: $b_{u}$
Can you write Python program for it?
 Write me a the Python program you requested?
assistant
#Here is the Python program you requested.

class SimplexProblem():

    def __init__(self, c=None, A=None, b=None, A_l=None, b_l = None):

        if (A_l is None and  not (A is None) ):

            self.b = b
            self.artf_num = A.shape[0]
            z = np.eye(self.artf_num)
            self.A = np.concatenate((A,z), axis = 1)
            self.c = np.concatenate((c, np.ones((self.artf_num))), axis=0)
            self.slack_num = 0

            self.num_var = self.A.shape[1]

        elif (A is None and  not (A_l is None)):

            self.slack_num = A_l.shape[0]
            s = np.eye(self.slack_num)
            self.A = np.concatenate((A_l,s), axis = 1)
            self.b=b_l
            self.artf_num = 0
            self.c = np.concatenate((c, np.zeros((self.slack_num))), axis=0)

            self.num_var = self.A.shape[1]

        elif (not (A is None) and  not (A_l is None)):

            self.slack_num = A_l.shape[0]
            s = np.eye(self.slack_num)
            s_ = np.zeros( (A.shape[0], self.slack_num) )
            self.artf_num = A.shape[0]
            z = np.eye(self.artf_num)
            z_ =  np.zeros( (A_l.shape[0], self.artf_num) )
            A_ = np.concatenate((A, z), axis=1)
            A_ = np.concatenate((A_, s_), axis=1)
            A_l_ = np.concatenate((A_l, z_), axis=1)
            A_l_ = np.concatenate((A_l_, s), axis=1)
            self.A = np.concatenate((A_,A_l_), axis=0)
            self.b = np.concatenate((b,b_l), axis=0)
            self.c = np.concatenate((c, 1000000*np.ones((self.artf_num)),
                                     np.zeros(self.slack_num)), axis=0)

            self.num_var = self.A.shape[1]

    def solve(self):

        x_b, x_n, x_b_val = self.init_base()
        opt = False
        z = 0

        ix=1
        while not opt:

            x_b, x_n, x_b_val, z, opt, status = self.iterate(x_b,x_n)

            ix+=1

        return x_b, x_n, x_b_val, z, status

    def init_base(self):

        x_b = [i for i in range(self.num_var - (self.artf_num+self.slack_num),
                   ...