diff --git a/MILP-demo.ipynb b/MILP-demo.ipynb
index 737edd5..d9bbbe8 100644
--- a/MILP-demo.ipynb
+++ b/MILP-demo.ipynb
@@ -70,7 +70,9 @@
     }
    ],
    "source": [
-    "c = -np.array([1, 2, 2])\n",
+    "## constant value in objective\n",
+    "\n",
+    "c = -np.array([1, 2, 2])  \n",
     "A = np.array([[-1, 1, 1], [3, 2, -1], [1, 1, 1], [2, 3, 3]])\n",
     "b_u = np.array([1, 12, 10, np.inf])\n",
     "b_l = np.array([-np.inf, -np.inf, -np.inf, 12])\n",
@@ -87,7 +89,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "We see the MILP solver tells us the object function is maximized when $x_1 = 6, x_2 = 0, x_3 = 7$.\n",
+    "We see the MILP solver tells us the object function is maximized when $x_1 = 5, x_2 = 0, x_3 = 5$.\n",
     "\n",
     "As the next step, let's create a corresponding `QuadraticProgram` class in `qiskit_optimization`."
    ]
@@ -125,7 +127,7 @@
    ],
    "source": [
     "## Consider the possibility of using sparse matrix(to_dict)\n",
-    "\n",
+    "## 1e20=inf\n",
     "qp = QuadraticProgram('example-1')\n",
     "qp.integer_var(name='x1')\n",
     "qp.integer_var(name='x2')\n",
@@ -202,6 +204,9 @@
     "\n",
     "\n",
     "## Check objective is linear\n",
+    "from types import NoneType\n",
+    "\n",
+    "\n",
     "if qp.objective.quadratic.to_dict()!={}:\n",
     "    raise QiskitError('Obejective function is not linear!')\n",
     "\n",
@@ -213,7 +218,7 @@
     "sense = qp.objective.sense.value\n",
     "\n",
     "## cost function for milp solver\n",
-    "c_qp = qp.objective.linear.to_array() * sense\n",
+    "c_qp = qp.objective.linear.to_array() * sense  \n",
     "\n",
     "## constraints for milp solver\n",
     "for i, constraint in enumerate(qp.linear_constraints):\n",
@@ -226,19 +231,50 @@
     "        bl_qp = np.array([constraint_value if constraint_sense==1 else -np.inf])\n",
     "        bu_qp = np.array([constraint_value if constraint_sense==0 else np.inf])\n",
     "    else:\n",
-    "        A_qp = np.vstack((A_qp,constraint_array))\n",
+    "        A_qp = np.vstack((A_qp,constraint_array))  ## Not efficient. Use list directly.\n",
     "        bl_qp = np.append(bl_qp, [constraint_value if constraint_sense==1 else -np.inf])\n",
     "        bu_qp = np.append(bu_qp, [constraint_value if constraint_sense==0 else np.inf])\n",
     "\n",
     "constraints = LinearConstraint(A_qp, bl_qp, bu_qp)\n",
     "\n",
     "## integrity for milp solver\n",
+    "## Use Enum and VarType to compare\n",
     "integrality = np.array([ 1 if variable.vartype.value==2 else 0 for variable in qp.variables]) ## check on other vartype!\n",
     "\n",
     "raw_res = milp(c=c_qp, constraints=constraints, integrality=integrality)\n",
     "\n",
     "print(raw_res)\n",
-    "    "
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "## Sparse converter based on to_dict"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
+   "metadata": {},
+   "outputs": [
+    {
+     "ename": "AttributeError",
+     "evalue": "'QuadraticProgram' object has no attribute 'constraints'",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
+      "Cell \u001b[0;32mIn [37], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mqp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mconstraints\u001b[49m\n",
+      "\u001b[0;31mAttributeError\u001b[0m: 'QuadraticProgram' object has no attribute 'constraints'"
+     ]
+    }
+   ],
+   "source": [
+    "qp.linear_constraints.sense"
    ]
   },
   {