Question No. 1

import numpy as np


maximize=[1,3]

constraintA=[10,5,4]
constraintB=[(1,2),(1,0),(0,1)]


class LPsolver():

    def solve(self,x,y,z):   
        lx=len(x)
        ly=len(y)
        arr=np.array(z)
        arr=np.concatenate((arr,np.identity(len(y))),1)
        y=np.array(y)
        a=[0]*lx

        arr=np.insert(arr,lx+ly,y,1)
        B=np.array([0]*ly)
        C=np.array(x+[0]*ly)
        bx=range(lx,lx+ly)
        while(1):
            maxp=[]
            minp=[]
            for i in range(lx+ly):
                maxp.append(C[i]-np.dot(B,arr[:,i]))


            z=maxp.index(max(maxp))

            if maxp[z]<=0:
                break
            for i in range(ly):
                if arr[i,z]!=0:
                    minp.append(arr[i,-1]/arr[i,z])
                else:
                    minp.append(10000000000)
            q=filter(lambda x:x>0,minp)
            if q==[]:
                return "unbounded function"
                break
            r=minp.index(min(q))

            B[r]=C[z]
            bx[r]=z
            arr[r,:]=arr[r,:]/arr[r,z]
            for i in range(ly):
                if(i!=r):
                    arr[i,:]=arr[i,:]-(arr[i,z]/arr[r,z])*arr[r,:]

        for i in range(len(bx)):
            if bx[i]<lx:
                a[bx[i]]=arr[i,-1]
        a=map(int,a)

        a.append(sum([a[i]*x[i] for i in range(lx)]))
        return a


lps=LPsolver()
solution=lps.solve(maximize,constraintA,constraintB)
print(solution)