#visualize solution g = np.linspace(0,5,200) x,y = np.meshgrid(g,g) obj = 0.5*(x**2+y**2)-2*x+2*y plt.imshow(((6*x+4*y<=24)&(x+2*y<=6)&(-x+y<=1)&(y<=2)&(x>=0)&(y>=0)).astype(int), extent=(x.min(),x.max(),y.min(),y.max()),origin='lower',cmap='Greys',alpha=0.3); #plot constraints x0 = np.linspace(0, 5, 2000) y0 = 6-1.5*x0 # 6*x+4*y<=24 y1 = 3-0.5*x0 # x+2*y<=6 y2 = 1+x0 # -x+y<=1 y3 = (x0*0) + 2 # y <= 2 y4 = x0*0 # x >= 0 plt.plot(x0, y0, label=r'$6x+4y\leq24$') plt.plot(x0, y1, label=r'$x+2y\leq6$') plt.plot(x0, y2, label=r'$-x+y\leq1$') plt.plot(x0, 2*np.ones_like(x0), label=r'$y\leq2$') plt.plot(x0, y4, label=r'$x\geq0$') plt.plot([0,0],[0,3], label=r'$y\geq0$') xv = [0,0,1,2,3,4,0]; yv = [0,1,2,2,1.5,0,0] plt.plot(xv,yv,'ko--',markersize=7,linewidth=2) for i in range(len(xv)): plt.text(xv[i]+0.1,yv[i]+0.1,f'({xv[i]},{yv[i]})') #objective contours CS = plt.contour(x,y,obj,np.arange(1,7)) plt.clabel(CS, inline=1, fontsize=10) plt.xlim(0,5); plt.ylim(0,3); plt.grid(); plt.tight_layout() plt.legend(loc=1); plt.xlabel('x'); plt.ylabel('y') plt.show()