diff --git a/A4/CSC_373_EC3.ipynb b/A4/CSC_373_EC3.ipynb
index f33088e..8bffdd6 100644
--- a/A4/CSC_373_EC3.ipynb
+++ b/A4/CSC_373_EC3.ipynb
@@ -2,7 +2,7 @@
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@@ -143,7 +143,7 @@
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@@ -230,7 +230,7 @@
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@@ -263,7 +263,7 @@
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@@ -302,7 +302,7 @@
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@@ -432,7 +432,7 @@
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@@ -475,7 +475,7 @@
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+      "execution_count": 6,
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@@ -3155,9 +3155,9 @@
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@@ -5843,9 +5843,9 @@
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-              "var gd = document.getElementById('f8bba3a2-0d4f-4f2b-843d-f7683c32b46a');\n",
+              "var gd = document.getElementById('da4954f6-c291-489e-b73d-eb33abe58e52');\n",
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@@ -5890,7 +5890,7 @@
     },
     {
       "cell_type": "code",
-      "execution_count": 7,
+      "execution_count": 8,
       "id": "574b5079-95d5-4936-8a3a-05cab65c7957",
       "metadata": {
         "colab": {
@@ -8542,9 +8542,9 @@
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               "                            \n",
-              "var gd = document.getElementById('88c05bf6-0203-4c1a-9abc-66becaab72ff');\n",
+              "var gd = document.getElementById('4f14aed4-1df9-44a7-a01b-1d6a75e5b92f');\n",
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@@ -8596,7 +8596,7 @@
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     {
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-      "execution_count": 8,
+      "execution_count": 9,
       "id": "efc93e0c-e9ce-442f-9bcd-b952f600cc31",
       "metadata": {
         "colab": {
@@ -8628,7 +8628,7 @@
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-          "execution_count": 8,
+          "execution_count": 9,
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@@ -8662,19 +8662,19 @@
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     {
       "cell_type": "code",
-      "execution_count": 9,
+      "execution_count": 50,
       "id": "84ab68a4-8efa-48ba-83e3-26eb8323be7f",
       "metadata": {
         "id": "84ab68a4-8efa-48ba-83e3-26eb8323be7f"
       },
       "outputs": [],
       "source": [
-        "cs_students, business_students = get_random_responses(30, seed=\"replace with your groups UTorIDs\")"
+        "cs_students, business_students = get_random_responses(4, seed=\"replace with your groups UTorIDs\")"
       ]
     },
     {
       "cell_type": "code",
-      "execution_count": 10,
+      "execution_count": 51,
       "id": "14557dcf-ec81-4618-9701-427c33268e1e",
       "metadata": {
         "colab": {
@@ -8690,7 +8690,7 @@
               "Response(student_id='0', availability={'Sunday_PM', 'Monday_PM', 'Saturday_AM'})"
             ]
           },
-          "execution_count": 10,
+          "execution_count": 51,
           "metadata": {},
           "output_type": "execute_result"
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@@ -8701,7 +8701,7 @@
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     {
       "cell_type": "code",
-      "execution_count": 11,
+      "execution_count": 52,
       "id": "_bFZl5lUEvg7",
       "metadata": {
         "colab": {
@@ -8718,7 +8718,7 @@
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-          "execution_count": 11,
+          "execution_count": 52,
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@@ -8729,7 +8729,7 @@
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     {
       "cell_type": "code",
-      "execution_count": 12,
+      "execution_count": 53,
       "id": "dOa40fmkEyjh",
       "metadata": {
         "colab": {
@@ -8745,7 +8745,7 @@
               "{'Monday_PM', 'Saturday_AM', 'Sunday_PM'}"
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-          "execution_count": 12,
+          "execution_count": 53,
           "metadata": {},
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@@ -8774,7 +8774,7 @@
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     {
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-      "execution_count": 13,
+      "execution_count": 54,
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         "id": "55b2c4b2-7dae-4b9d-a298-d67fa5173826"
@@ -8784,23 +8784,9 @@
           "name": "stdout",
           "output_type": "stream",
           "text": [
-            "Students Matched: 15\n",
+            "Students Matched: 1\n",
             "Student ID Matches:\n",
-            "\t('15', '8')\n",
-            "\t('16', '4')\n",
-            "\t('17', '13')\n",
-            "\t('18', '12')\n",
-            "\t('19', '5')\n",
-            "\t('20', '14')\n",
-            "\t('21', '11')\n",
-            "\t('22', '10')\n",
-            "\t('23', '3')\n",
-            "\t('24', '1')\n",
-            "\t('25', '9')\n",
-            "\t('26', '6')\n",
-            "\t('27', '2')\n",
-            "\t('28', '0')\n",
-            "\t('29', '7')\n"
+            "\t('2', '0')\n"
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               "                            \n",
-              "var gd = document.getElementById('f945af5a-de08-4fb7-ab3f-1d801c1910fe');\n",
+              "var gd = document.getElementById('3712b8b3-f257-42a1-bce0-1f24836feb87');\n",
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@@ -29693,12 +10199,65 @@
     },
     {
       "cell_type": "code",
-      "execution_count": 21,
+      "execution_count": 62,
       "id": "39b97a8f-84a8-4fc1-8eaa-5487423f042e",
       "metadata": {
         "id": "39b97a8f-84a8-4fc1-8eaa-5487423f042e"
       },
       "outputs": [
+        {
+          "name": "stdout",
+          "output_type": "stream",
+          "text": [
+            "Possible student pairings: 4\n",
+            "c: \n",
+            "[1. 1. 1. 1. 1. 1. 1. 1.]\n",
+            "A: \n",
+            "[[  1.   0.   0.   0.   0.   0.   0.   0.]\n",
+            " [  0.   1.   0.   0.   0.   0.   0.   0.]\n",
+            " [  0.   0.   1.   0.   0.   0.   0.   0.]\n",
+            " [  0.   0.   0.   1.   0.   0.   0.   0.]\n",
+            " [  1.   0.   0.   0. -14.  -0.  -0.  -0.]\n",
+            " [  0.   1.   0.   0.  -0. -14.  -0.  -0.]\n",
+            " [  0.   0.   1.   0.  -0.  -0. -14.  -0.]\n",
+            " [  0.   0.   0.   1.  -0.  -0.  -0. -14.]\n",
+            " [  0.   0.   0.   0.   1.   0.   0.   0.]\n",
+            " [  0.   0.   0.   0.   0.   1.   0.   0.]\n",
+            " [  0.   0.   0.   0.   0.   0.   1.   0.]\n",
+            " [  0.   0.   0.   0.   0.   0.   0.   1.]\n",
+            " [ -1.  -0.  -0.  -0.   1.   0.   0.   0.]\n",
+            " [ -0.  -1.  -0.  -0.   0.   1.   0.   0.]\n",
+            " [ -0.  -0.  -1.  -0.   0.   0.   1.   0.]\n",
+            " [ -0.  -0.  -0.  -1.   0.   0.   0.   1.]]\n",
+            "b: [1. 1. 0. 0. 0. 0. 0. 0. 1. 1. 1. 1. 0. 0. 0. 0.]\n",
+            "        message: Optimization terminated successfully. (HiGHS Status 7: Optimal)\n",
+            "        success: True\n",
+            "         status: 0\n",
+            "            fun: -4.0\n",
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               "                            \n",
-              "var gd = document.getElementById('70dc9aaa-fec6-4a58-b1b3-913d2083f238');\n",
+              "var gd = document.getElementById('bb8e06f5-6f10-4b31-988e-3e75a6de3873');\n",
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@@ -50528,27 +11607,62 @@
         }
       ],
       "source": [
+        "# https://cs.stackexchange.com/a/12118 was used to cast to boolean\n",
+        "\n",
         "# Generating Order for Tracking Purposes (not necessarily needed) (can be replaced with simple 15*15)\n",
         "possible_student_pairings = []\n",
         "for cs_student in cs_students:\n",
         "    for business_student in business_students:\n",
         "        possible_student_pairings.append((cs_student.student_id, business_student.student_id))\n",
+        "print(f\"Possible student pairings: {len(possible_student_pairings)}\")\n",
+        "# Setting up objective coefficients and constraints\n",
         "\n",
-        "# Setting up objective coefficients\n",
+        "c = np.concatenate((\n",
+        "    np.ones(len(possible_student_pairings)), # flow variables (X)\n",
+        "    np.ones(len(possible_student_pairings))   # usage boolean Y (should these be zeros?)\n",
+        "))\n",
         "\n",
-        "c = np.ones((len(possible_student_pairings))) # Coefficients all 1\n",
+        "import sys\n",
+        "np.set_printoptions(threshold=sys.maxsize)\n",
+        "print(f\"c: \\n{c}\")\n",
         "\n",
-        "A = np.identity(len(possible_student_pairings)) # flow coefficients also 1, each row represents one edge, thus all non corresponding variables have coefficient 0\n",
-        "b = np.zeros((len(possible_student_pairings))) # Assume edge has no capacity\n",
+        "A = np.vstack((\n",
+        "    np.hstack((np.identity(len(possible_student_pairings)), np.zeros((len(possible_student_pairings), len(possible_student_pairings))))), # flow coefficients 1, row represents one edge, non corresponding coefficients to that row are 0, thus, identity.\n",
+        "    np.hstack((np.identity(len(possible_student_pairings)), -len(WORK_TIMES) * np.identity(len(possible_student_pairings)))), # cast all edge values to boolean by constraining x - u*Y <= 0 set up below\n",
+        "    np.hstack((np.zeros((len(possible_student_pairings), len(possible_student_pairings))), np.identity(len(possible_student_pairings)))), # constrain boolean variable Y <= 1\n",
+        "    np.hstack((-np.identity(len(possible_student_pairings)), np.identity(len(possible_student_pairings)))), # constrain boolean variable Y <= X \n",
+        "    # np.zeros((len(cs_students), len(possible_student_pairings) + len(possible_student_pairings))) # any edge can only be used once\n",
+        "))\n",
+        "print(f\"A: \\n{A}\")\n",
+        "\n",
+        "b = np.concatenate((\n",
+        "    np.zeros(len(possible_student_pairings)), # flow capacities for X\n",
+        "    np.zeros(len(possible_student_pairings)), #  X - UY <= 0 cast to boolean\n",
+        "    np.ones(len(possible_student_pairings)), # Y <= 1 cast to boolean\n",
+        "    np.zeros(len(possible_student_pairings)), # Y - X <= 0 cast to boolean\n",
+        "    # np.ones(len(cs_students)) # Single match Y sum ensures at most one pairing per cs student\n",
+        "))\n",
+        "\n",
+        "## Set up xor or no match\n",
+        "# for cs_student_row in range(len(cs_students)): # At most one edge per student (sets up for the last set of matrices)\n",
+        "#     row_start = len(possible_student_pairings) + len(possible_student_pairings) + len(possible_student_pairings)\n",
+        "#     for business_index in range(len(business_students)):\n",
+        "#         A[row_start + cs_student_row][len(possible_student_pairings) + cs_student_row * len(business_students) + business_index] = 1\n",
+        "\n",
+        "## Calculate maximum overlaps\n",
         "for cs_index, cs_student in enumerate(cs_students): # order is deterministic (list)\n",
         "    for business_index, business_student in enumerate(business_students): # order is deterministic (list)\n",
         "        pairing_index = cs_index * len(cs_students) + business_index\n",
-        "        for availability in cs_student.availability:\n",
+        "        for availability in cs_student.availability: # O(1) since availability must be less than or equal to constant number of time slots\n",
         "            if availability in business_student.availability:\n",
         "                b[pairing_index] = b[pairing_index] + 1\n",
         "\n",
+        "print(f\"b: {b}\")\n",
+        "\n",
         "# Run optimization\n",
         "optimization_results = linprog(-c, A_ub=A, b_ub=b, bounds=(0,None))\n",
+        "print(optimization_results)\n",
+        "print(optimization_results.x)\n",
         "\n",
         "# Retrieve optimized values and calculate matching\n",
         "t2_matching = []\n",
@@ -50559,7 +11673,8 @@
         "    best_business_match_index = None\n",
         "    for business_index, business_student in enumerate(business_students): # order is deterministic (list)\n",
         "        if business_students_matched[business_index]:\n",
-        "            continue # If this business student has already matched optimally, we skip them\n",
+        "            print(\"ERROR, duplicate found. Should not be possible\")\n",
+        "            continue \n",
         "        pairing_index = cs_index * len(cs_students) + business_index\n",
         "        if optimization_results.x[pairing_index] > best_business_match_score:\n",
         "            best_business_match_student = business_student\n",