import numpy as np
from numpy.linalg import inv
import sys

def f(x):
    return 2 * x[0] + 3 * x[1] - 4 * x[2]
    
def simplex(A0, b0, c0):
    n = 4
    m = 2
    shape = A0.shape
    B = A0[:, 0:m]
    N = A0[:, m:n]
    cB = c0[:, 0:m]
    cN = c0[:, m:n]
    x = np.zeros((1, n))
    
    pi = np.dot(cB, inv(B))
    z = np.dot(pi, N)
    d = z - cN
    beta = np.transpose(np.dot(inv(B), np.transpose(b)))
    q = d[0].argmin()
    
    if d[0][q] > 0:
        buf = np.zeros((1, m))
        i = m
        while i < n:
            buf[0][i-m] = x[0][i]
            i += 1
        buf = beta - np.dot(np.dot(inv(B), N), np.transpose(buf))
        i = 0
        while i < m:
            x[0][i] = buf[0][i] 
            i += 1
        return x
        
    alphaQ = np.dot(inv(B), N[:, q])
    minP = -1
    minmin = sys.float_info.max
    i = 0
    while i < m:
        if alphaQ[i] > (1 ** (-10)) and beta[i] / alphaQ[i] < minmin:
            minmin = beta[i] / alphaQ[i]
            minP = i
    if minP < 0:
        return " :( "
    x[0][q + m] = minmin
    B[:, minP] = N[:, q]
    
    
c = np.array([[2, 3, -4, 0]])

A = np.array([[-1, 2, 3, 0], \
               [3, 1, 0, 1]])  

b = np.array([[24, 32]])

x = simplex(A, b, c)
print f(x[0])