diff --git a/examples/utility_function_demo.ipynb b/examples/utility_function_demo.ipynb
new file mode 100644
index 0000000..ee54102
--- /dev/null
+++ b/examples/utility_function_demo.ipynb
@@ -0,0 +1,607 @@
+{
+  "nbformat": 4,
+  "nbformat_minor": 0,
+  "metadata": {
+    "colab": {
+      "provenance": [],
+      "authorship_tag": "ABX9TyMLWlCaXa90pQB7POCVUrPr",
+      "include_colab_link": true
+    },
+    "kernelspec": {
+      "name": "python3",
+      "display_name": "Python 3"
+    },
+    "language_info": {
+      "name": "python"
+    }
+  },
+  "cells": [
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "view-in-github",
+        "colab_type": "text"
+      },
+      "source": [
+        "<a href=\"https://colab.research.google.com/github/cmudrc/sae/blob/master/examples/utility_function_demo.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "This notebook demonstrates three unique ways to compute the utility of a vehicle. The outcomes from each case may or may not align! The three approaches are:\n",
+        "1. Partworth utility over a measure of quality for every unique component of the car\n",
+        "2. Quadratic utility over a measure of quality for every unique component of the car\n",
+        "2. Quadratic utility over the performance attributes of the car, each of which relies on several components"
+      ],
+      "metadata": {
+        "id": "NdwyMZ8Pn_kB"
+      }
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "## Install and Import"
+      ],
+      "metadata": {
+        "id": "HAJrSacGn5vz"
+      }
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 1,
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "8f9JU38Feqxv",
+        "outputId": "6e758127-832d-4ca5-d675-ff04f3d8abbd"
+      },
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "Collecting git+https://github.com/cmudrc/sae.git\n",
+            "  Cloning https://github.com/cmudrc/sae.git to /tmp/pip-req-build-m8fb5j5i\n",
+            "  Running command git clone --filter=blob:none --quiet https://github.com/cmudrc/sae.git /tmp/pip-req-build-m8fb5j5i\n",
+            "  Resolved https://github.com/cmudrc/sae.git to commit ce6a789e0b810785ba4fb570dcbea5b40848508f\n",
+            "  Preparing metadata (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
+            "Requirement already satisfied: numpy in /usr/local/lib/python3.10/dist-packages (from sae==0.1.0) (1.23.5)\n",
+            "Requirement already satisfied: scipy in /usr/local/lib/python3.10/dist-packages (from sae==0.1.0) (1.11.4)\n",
+            "Requirement already satisfied: pandas in /usr/local/lib/python3.10/dist-packages (from sae==0.1.0) (1.5.3)\n",
+            "Requirement already satisfied: openpyxl in /usr/local/lib/python3.10/dist-packages (from sae==0.1.0) (3.1.2)\n",
+            "Requirement already satisfied: et-xmlfile in /usr/local/lib/python3.10/dist-packages (from openpyxl->sae==0.1.0) (1.1.0)\n",
+            "Requirement already satisfied: python-dateutil>=2.8.1 in /usr/local/lib/python3.10/dist-packages (from pandas->sae==0.1.0) (2.8.2)\n",
+            "Requirement already satisfied: pytz>=2020.1 in /usr/local/lib/python3.10/dist-packages (from pandas->sae==0.1.0) (2023.3.post1)\n",
+            "Requirement already satisfied: six>=1.5 in /usr/local/lib/python3.10/dist-packages (from python-dateutil>=2.8.1->pandas->sae==0.1.0) (1.16.0)\n",
+            "Building wheels for collected packages: sae\n",
+            "  Building wheel for sae (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
+            "  Created wheel for sae: filename=sae-0.1.0-py3-none-any.whl size=26146 sha256=c875573c5df75f9da76c8c09fd28182801e67aa8f7732e387398a756caff1d82\n",
+            "  Stored in directory: /tmp/pip-ephem-wheel-cache-5rgx4t57/wheels/8d/20/04/8e9bbfdfb118386e3253608654c865b42b674862a738800cfb\n",
+            "Successfully built sae\n",
+            "Installing collected packages: sae\n",
+            "Successfully installed sae-0.1.0\n"
+          ]
+        }
+      ],
+      "source": [
+        "!pip install git+https://github.com/cmudrc/sae.git"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "import numpy\n",
+        "from numpy.typing import NDArray\n",
+        "from typing import Tuple\n",
+        "import sae"
+      ],
+      "metadata": {
+        "id": "io0PLTfGe9b2"
+      },
+      "execution_count": 10,
+      "outputs": []
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "## Generate two random cars for us to examine"
+      ],
+      "metadata": {
+        "id": "G0M5Q8F3nzbd"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "example_car_1 = sae.Car()\n",
+        "example_car_2 = sae.Car()"
+      ],
+      "metadata": {
+        "id": "RtEDRw4qetSW"
+      },
+      "execution_count": 3,
+      "outputs": []
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "# Simulating Random Customers with Partworth Utility"
+      ],
+      "metadata": {
+        "id": "9U4Bk3q9hL-m"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "# Get weights for a random customer that define their preferences\n",
+        "weights = numpy.random.rand(10)\n",
+        "print(weights)"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "Vb3JO1FZfms4",
+        "outputId": "4834db10-89b2-450c-8b33-d1cb34629274"
+      },
+      "execution_count": 4,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "[0.80796276 0.22177387 0.8828941  0.38631095 0.90739784 0.5546031\n",
+            " 0.83253125 0.36430607 0.6914742  0.10234462]\n"
+          ]
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "# Evaluate the car with respect to those weights. Note that the returned values\n",
+        "# are scaled according to approximate bounds and represent utility*-1 to provide\n",
+        "# an implicit minimization framing\n",
+        "example_car_1.partworth_objectives(weights=weights)"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "_mwPC6Bqgq37",
+        "outputId": "448a2056-c491-4c8d-9fff-bdef572f1f7d"
+      },
+      "execution_count": 5,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "(-1.0028852531019703,\n",
+              " array([-0.00828908, -0.19115229, -0.00247374, -0.01126424, -0.03145214,\n",
+              "        -0.41163063, -0.3281428 , -0.3718878 , -0.28225456, -0.84603138]))"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 5
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "example_car_2.partworth_objectives(weights=weights)"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "LFzk52iPiK9y",
+        "outputId": "f3ebd06b-733f-4f3d-97a2-acc1941e560b"
+      },
+      "execution_count": 6,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "(-1.234540242718953,\n",
+              " array([-0.77745905, -0.02698055, -0.1038017 , -0.01007241, -0.00431661,\n",
+              "        -0.14338959, -0.24939046, -0.28994642, -0.10844283, -0.32420369]))"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 6
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "# Assuming the customer acts rationally with respect to this preference model,\n",
+        "# they should buy the following car:\n",
+        "\"Car 1\" if example_car_1.partworth_objectives(weights=weights)[0] < example_car_2.partworth_objectives(weights=weights)[0] else \"Car 2\""
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 35
+        },
+        "id": "2oeLDHcWilHv",
+        "outputId": "6537eb9a-5631-4c53-e0bc-0d71aae84bb2"
+      },
+      "execution_count": 7,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "'Car 2'"
+            ],
+            "application/vnd.google.colaboratory.intrinsic+json": {
+              "type": "string"
+            }
+          },
+          "metadata": {},
+          "execution_count": 7
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "# Simulating Random Customers with Quadratic Utility over Parts"
+      ],
+      "metadata": {
+        "id": "gj1X6sp1jr_N"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "# The point of simulating customers with more complex utility functions is that\n",
+        "# sometimes more isn't necessarily better! For this"
+      ],
+      "metadata": {
+        "id": "cCm85pRGjW3C"
+      },
+      "execution_count": null,
+      "outputs": []
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "def quadratic_utility_over_parts(car: sae.Car, weights: NDArray) -> Tuple[float, list]:\n",
+        "    partworth = -car.partworth_objectives()[1]\n",
+        "    quadratic_partworth = []\n",
+        "    quadratic_utility = 0.0\n",
+        "    for idx, part in enumerate(list(partworth)):\n",
+        "        quadratic_part = weights[idx,0] + weights[idx,1]*part + weights[idx,2]*part*part\n",
+        "        quadratic_utility -= quadratic_part\n",
+        "        quadratic_partworth.append(-quadratic_part)\n",
+        "\n",
+        "    return (quadratic_utility, quadratic_partworth)"
+      ],
+      "metadata": {
+        "id": "Px2NqKz4kJaZ"
+      },
+      "execution_count": 23,
+      "outputs": []
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "# Define the mean form for our weights - this should yield a \"leveling out\" as\n",
+        "# parts become more performant\n",
+        "mean = numpy.array([[0.0, 2.0, -1.0]] * 10)"
+      ],
+      "metadata": {
+        "id": "wYr9zyXymW2P"
+      },
+      "execution_count": 24,
+      "outputs": []
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "# We can now add some variance to each of the weights\n",
+        "weights = mean + 0.1*numpy.random.randn(10, 3)"
+      ],
+      "metadata": {
+        "id": "AnrK7nRanAL4"
+      },
+      "execution_count": 26,
+      "outputs": []
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "# With these new weights, we can compute the utility\n",
+        "quadratic_utility_over_parts(example_car_1, weights)"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "r5iBMkCrmdkz",
+        "outputId": "eeb631e0-016d-4686-a496-eb01cb89d0e2"
+      },
+      "execution_count": 30,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "(-4.071488205948333,\n",
+              " [-0.03126401575296759,\n",
+              "  -0.49089609191384587,\n",
+              "  0.10999728521578471,\n",
+              "  -0.1251560690047339,\n",
+              "  -0.23026173716869616,\n",
+              "  -0.8025663995233542,\n",
+              "  -0.6015243863484405,\n",
+              "  -0.6218019671511774,\n",
+              "  -0.4599948061092836,\n",
+              "  -0.8180200181916184])"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 30
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "quadratic_utility_over_parts(example_car_2, weights)"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "foj8zMwCnW7I",
+        "outputId": "05b55459-3bcc-4bc4-aa56-840a8f23d83d"
+      },
+      "execution_count": 34,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "(-3.5374681841143047,\n",
+              " [-0.9674580251962474,\n",
+              "  -0.17123561612296972,\n",
+              "  -0.091656557801661,\n",
+              "  -0.1227515219969897,\n",
+              "  -0.1722880595563746,\n",
+              "  -0.3619720050640406,\n",
+              "  -0.47527137316762497,\n",
+              "  -0.5237436374864741,\n",
+              "  -0.17106735660811145,\n",
+              "  -0.4800240311138118])"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 34
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "# Assuming the customer acts rationally with respect to this preference model,\n",
+        "# they should buy the following car:\n",
+        "\"Car 1\" if quadratic_utility_over_parts(example_car_1, weights)[0] < quadratic_utility_over_parts(example_car_2, weights)[0] else \"Car 2\""
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 35
+        },
+        "id": "nglaLu6SmzNn",
+        "outputId": "6716923c-847e-4ef0-d23e-155e42159ced"
+      },
+      "execution_count": 32,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "'Car 1'"
+            ],
+            "application/vnd.google.colaboratory.intrinsic+json": {
+              "type": "string"
+            }
+          },
+          "metadata": {},
+          "execution_count": 32
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "# Simulating Random Customers with Quadratic Utility over Performance"
+      ],
+      "metadata": {
+        "id": "KaWYPF9fnaq0"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "# The point of simulating customers with more complex utility functions is that\n",
+        "# sometimes more isn't necessarily better!"
+      ],
+      "metadata": {
+        "id": "h_OIoZ-Enaq1"
+      },
+      "execution_count": null,
+      "outputs": []
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "def quadratic_utility_over_performance(car: sae.Car, weights: NDArray) -> Tuple[float, list]:\n",
+        "    partworth = car.objectives()[1]\n",
+        "    quadratic_partworth = []\n",
+        "    quadratic_utility = 0.0\n",
+        "    for idx, part in enumerate(list(partworth)):\n",
+        "        quadratic_part = weights[idx,0] + weights[idx,1]*part + weights[idx,2]*part*part\n",
+        "        quadratic_utility -= quadratic_part\n",
+        "        quadratic_partworth.append(-quadratic_part)\n",
+        "\n",
+        "    return (quadratic_utility, quadratic_partworth)"
+      ],
+      "metadata": {
+        "id": "ToqHACc5naq1"
+      },
+      "execution_count": 42,
+      "outputs": []
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "# Define the mean form for our weights - this should yield a \"leveling out\" as\n",
+        "# parts become more performant\n",
+        "mean = numpy.array([[0.0, 2.0, -1.0]] * 11)"
+      ],
+      "metadata": {
+        "id": "FFNf9K4Enaq1"
+      },
+      "execution_count": 43,
+      "outputs": []
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "# We can now add some variance to each of the weights\n",
+        "weights = mean + 0.1*numpy.random.randn(11, 3)"
+      ],
+      "metadata": {
+        "id": "LOVcbDAInaq1"
+      },
+      "execution_count": 44,
+      "outputs": []
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "# With these new weights, we can compute the utility\n",
+        "quadratic_utility_over_performance(example_car_1, weights)"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "outputId": "bc823076-4c76-4b93-abee-751324bbe014",
+        "id": "lKGb3qSonaq1"
+      },
+      "execution_count": 45,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "(-4.903078439305462,\n",
+              " [0.0981353783732669,\n",
+              "  -0.2994749708779486,\n",
+              "  -0.20648371506368626,\n",
+              "  -1.0953602066268822,\n",
+              "  -1.0351736151108994,\n",
+              "  -0.19673768920421758,\n",
+              "  -0.09611383594573847,\n",
+              "  -1.25267105164887,\n",
+              "  -0.14563029029530491,\n",
+              "  -0.1956765490085978,\n",
+              "  -0.4778918938965845])"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 45
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "quadratic_utility_over_performance(example_car_2, weights)"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "outputId": "2c9a4c41-d8f9-44e0-e8a4-9449173ecd6c",
+        "id": "tT8UiE2hnaq2"
+      },
+      "execution_count": 46,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "(-6.705037303255647,\n",
+              " [-0.0224891939112073,\n",
+              "  -0.8982419122961699,\n",
+              "  -0.7106703330066542,\n",
+              "  -0.7165058036911959,\n",
+              "  -1.034878063603879,\n",
+              "  -0.3989786308510101,\n",
+              "  -0.3858572049689103,\n",
+              "  -0.9292412429505923,\n",
+              "  -0.30438664934800563,\n",
+              "  -0.5783186742202403,\n",
+              "  -0.7254695944077834])"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 46
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "# Assuming the customer acts rationally with respect to this preference model,\n",
+        "# they should buy the following car:\n",
+        "\"Car 1\" if quadratic_utility_over_parts(example_car_1, weights)[0] < quadratic_utility_over_parts(example_car_2, weights)[0] else \"Car 2\""
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 35
+        },
+        "outputId": "c621c7dc-6059-42be-b064-c2edbbb91ca3",
+        "id": "lIpu96W1naq2"
+      },
+      "execution_count": 47,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "'Car 1'"
+            ],
+            "application/vnd.google.colaboratory.intrinsic+json": {
+              "type": "string"
+            }
+          },
+          "metadata": {},
+          "execution_count": 47
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [],
+      "metadata": {
+        "id": "d9hukZEmntiJ"
+      },
+      "execution_count": null,
+      "outputs": []
+    }
+  ]
+}
\ No newline at end of file