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Section 2
Discuss the characteristics of optimisation problems
What is optimisation?
Finds the optimal, or most efficient, way of using limited resources to achieve the objectives of an individual of a business.
Explore the use of linear programming (LP) in solving optimisation problems
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2Febcbe79c-91a8-4ed0-ab0f-fe197e1ff958%2FUntitled.png%3Ftable%3Dblock%26id%3Dba44fcea-41a9-4657-9cf4-fc1c4664ca0f%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725818400000%26signature%3DmG1bo3C6fUvP2F4GP1PnFTu7PAbqqVOglD5bMJlniGk?table=block&id=ba44fcea-41a9-4657-9cf4-fc1c4664ca0f&cache=v2)
- Understand the problem.
- Define the decision variables.
X_1 =number of Aqua-Spas to produce
X_2 =number of Hydro-Luxes to produce
- Define the objective function
MAX: 350X 1 + 300X 2
- Define the constraints
- For this step, there are types of constraints in other cases, namely Demand Constraints, Resource Constraints, and Non-negativity conditions (which the next step).
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2F29d7880c-c0eb-49c6-8aab-64c4c47ae246%2FUntitled.png%3Ftable%3Dblock%26id%3D1df5058d-5957-419b-aaa1-b189364954d9%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725818400000%26signature%3DoWtmjHp-5s3o4myA1PW9O_6K57iZzHuy_wCPiPBMc8E?table=block&id=1df5058d-5957-419b-aaa1-b189364954d9&cache=v2)
- Identify any upper or lower bounds on the decision variables.
X1 >= 0 && X2 >= 0
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2Fabb79e9a-2b81-4817-aa0d-7692e7effd19%2FUntitled.png%3Ftable%3Dblock%26id%3D0e09c5c4-01b1-4c63-9821-2312da1490bb%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725818400000%26signature%3D_oh_yFJkA8F9y9RWphm4K7dBrRCRiOwdfK7-n_sM6Yk?table=block&id=0e09c5c4-01b1-4c63-9821-2312da1490bb&cache=v2)
Solving LP problems using graphical approach
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2F95e7f9c8-231d-4cdc-b5c5-4b9bd37813af%2FUntitled.png%3Ftable%3Dblock%26id%3D5fd13656-8917-4d4b-9f3f-4370d9496260%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725818400000%26signature%3DS7JRTlgQkroTG6G6YsC5M3Gfo-Og9HJnRfrKAIQ0SEg?table=block&id=5fd13656-8917-4d4b-9f3f-4370d9496260&cache=v2)
![In Summary](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2F7de67790-9660-4918-9ca0-aa83f89b3d6f%2FUntitled.png%3Ftable%3Dblock%26id%3D9a3af409-ffd8-4557-b4d9-a30ae8894af1%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725818400000%26signature%3DOc4QTTaVPGVw6nrOKDPfNS-Zp_XjpzImwkxem6IEk3I?table=block&id=9a3af409-ffd8-4557-b4d9-a30ae8894af1&cache=v2)
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2Fe5fd62c9-6a34-4fa6-a300-ddc80c8ffc56%2FUntitled.png%3Ftable%3Dblock%26id%3D1eff239c-ecfa-4f30-b77b-849d4189877e%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725818400000%26signature%3Drzi845p1meKemUH3mlYaDAE1sKXCkyHyrs2jnX0oxn4?table=block&id=1eff239c-ecfa-4f30-b77b-849d4189877e&cache=v2)
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2F884fea56-896d-40fb-8130-bab7df3410fa%2FUntitled.png%3Ftable%3Dblock%26id%3D73cb1189-d343-4201-bc81-3e74b6e218a3%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725818400000%26signature%3DCK0Y5eGPTL4Sp6F9bygWR-F7274WGADdrW_hYrbhZ2M?table=block&id=73cb1189-d343-4201-bc81-3e74b6e218a3&cache=v2)
Special condition
Case 1: Alternate Optimal Solutions
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2Fe2cadb8f-b336-4d34-87a3-3563528a70f1%2FUntitled.png%3Ftable%3Dblock%26id%3D11c111fc-2534-44dd-8df0-529f1455aab9%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725818400000%26signature%3DCXDPpNdWTGXAOBzYMtWaSlyWIQUS68xfwTmni1h-jVY?table=block&id=11c111fc-2534-44dd-8df0-529f1455aab9&cache=v2)
Case 2: Redundant Constraint
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2Fcfe36483-c771-4824-a67f-8e6daa8eb742%2FUntitled.png%3Ftable%3Dblock%26id%3D4d55596e-75d2-4ba8-8df6-713c188d4dc5%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725818400000%26signature%3D0xEbTXScVL7EEL-LE7ypWMqgloiwSnTKuIUnX2sXtjg?table=block&id=4d55596e-75d2-4ba8-8df6-713c188d4dc5&cache=v2)
Case 3: Unbounded Solution
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2Fb9df9256-815f-484e-9af1-254b903a5ddb%2FUntitled.png%3Ftable%3Dblock%26id%3Dbd6a1133-7753-4e4c-a651-b34f2b7bb9cc%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725818400000%26signature%3DyUB64cuU7BU4U-KdtHYUhHbX0wbutDuPpaHdzUvnMqE?table=block&id=bd6a1133-7753-4e4c-a651-b34f2b7bb9cc&cache=v2)
Case 4: Infeasibility
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2F972372be-95ab-4373-b9f8-f64f129d431b%2FUntitled.png%3Ftable%3Dblock%26id%3D94ddd2ac-8bd3-4512-a156-f8e37c8218eb%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725818400000%26signature%3D-xdyShXnqP2VBW2-WdAUTWIdtv7Toxbv57i1Fi2tfDI?table=block&id=94ddd2ac-8bd3-4512-a156-f8e37c8218eb&cache=v2)
- Author:Jason Siu
- URL:https://jason-siu.com/a5710386b9674116bf5cd219298c4dbf
- Copyright:All articles in this blog, except for special statements, adopt BY-NC-SA agreement. Please indicate the source!
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