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Lecture: Blue Ridge Hot Tubs
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2Fb41242e0-978c-472a-9a0c-f36412e91471%2FUntitled.png%3Ftable%3Dblock%26id%3Dae682453-b31f-4c8f-aa7f-5cbed2d03b04%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725789600000%26signature%3Dz5ODkGOKRQrI0RQU8vny9EQaPstX3RVmsCRoIoQ7XgM?table=block&id=ae682453-b31f-4c8f-aa7f-5cbed2d03b04&cache=v2)
Solution
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2F8aa7334c-ca22-4114-b351-3158c442f6f5%2FUntitled.png%3Ftable%3Dblock%26id%3D267dade0-7bca-46e4-8781-33c956120973%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725789600000%26signature%3DdehDODkMF4egxrvDqzRQ5jA402wM_UEs4MpnG-1r7yE?table=block&id=267dade0-7bca-46e4-8781-33c956120973&cache=v2)
Solution using an Intuitive approach
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2F64423ed3-5d44-4944-9d8f-a420c7bad2e6%2FUntitled.png%3Ftable%3Dblock%26id%3De1d55fa9-0ce7-46a1-b172-cbf63caf194c%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725789600000%26signature%3DyNVrX6OxBdrbfZqJLwLzNHgjwA7UYLEZqwSnVB1PJKc?table=block&id=e1d55fa9-0ce7-46a1-b172-cbf63caf194c&cache=v2)
Solution using a Graphical approach
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2Fc2a79db3-2fab-4ab4-ad12-74c8139dff7f%2FUntitled.png%3Ftable%3Dblock%26id%3D4778d476-d2bb-421a-a1f8-0e281346202b%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725789600000%26signature%3DTawYVNvOG-UJpHQC-W23IklEEYzpMo3YIS7pI8ngPA0?table=block&id=4778d476-d2bb-421a-a1f8-0e281346202b&cache=v2)
Lab1 (A Maximisation Problem) Part A Q1:
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2F0f93a066-d704-4bf2-93d9-26e6578ab03c%2FUntitled.png%3Ftable%3Dblock%26id%3Db647da9c-cca9-492a-991a-1f8057e84214%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725789600000%26signature%3D2E7cAlBT8NBth8-D6tGuNtqk90Mv4tbXJrue2VJaKKU?table=block&id=b647da9c-cca9-492a-991a-1f8057e84214&cache=v2)
Solution
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2Fa35e07e7-2236-49dd-b1de-da12f8a09f51%2FUntitled.png%3Ftable%3Dblock%26id%3Db1bfa5da-ded3-47af-b286-a5093a001734%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725789600000%26signature%3DF4iIUNf0PknShad4F_gkYiXEskj6Xgx-wW0ZcNRte-Q?table=block&id=b1bfa5da-ded3-47af-b286-a5093a001734&cache=v2)
Lab1 (A Maximisation Problem) Part A Q2: [!obj. function]
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2F23afa971-d886-44d4-93b1-833664d70fb3%2FUntitled.png%3Ftable%3Dblock%26id%3D95965898-8798-4238-8dbb-89b9ea7c384a%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725789600000%26signature%3DzqV-q4QcP8AEP83qFAhDJd2GUijh2CtkyaofKVofybo?table=block&id=95965898-8798-4238-8dbb-89b9ea7c384a&cache=v2)
Solution
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2Fafdb5e6f-db80-4337-ad03-017a276f42bd%2FUntitled.png%3Ftable%3Dblock%26id%3Dbb3b34e9-1d60-403a-b34a-e9a20361dd61%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725789600000%26signature%3DFUXDokd9203wnO6N0ctrKSHHIRK6ogrOu29pF-gY50I?table=block&id=bb3b34e9-1d60-403a-b34a-e9a20361dd61&cache=v2)
Lab1 (A Minimisation Problem) Part A Q3:
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2Fb88900de-811c-4cbc-b99b-583b496697f4%2FUntitled.png%3Ftable%3Dblock%26id%3D24946dc5-1ac3-4ad1-b0dd-c8af11fbfb88%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725789600000%26signature%3DFFhU2k-j3WNd2cqNL-zcJpAy-8O6vGWPLBWrXxyY3mU?table=block&id=24946dc5-1ac3-4ad1-b0dd-c8af11fbfb88&cache=v2)
Solution
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2Fa8a20fcc-b616-434f-b170-62dab24e3f6d%2FUntitled.png%3Ftable%3Dblock%26id%3D6abf305f-8d89-46c8-a9ad-fcf4ef29c8d0%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725789600000%26signature%3DjHBpGFyVgyCtjnEKZa-uAahN5lhadvBxpb_zY5K9tA4?table=block&id=6abf305f-8d89-46c8-a9ad-fcf4ef29c8d0&cache=v2)
Lab1 (A Minimisation Problem) Part B Q1: [!Calculate ratio]
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2Fe13ca543-2d6f-496d-b8a2-f01fa79370b0%2FUntitled.png%3Ftable%3Dblock%26id%3D17db6866-f16d-4052-ad6d-41eb33817b44%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725789600000%26signature%3DjsU9Wnmcp5Un06mTacwU6IUV8O9dIIsPnU1AwWZLMto?table=block&id=17db6866-f16d-4052-ad6d-41eb33817b44&cache=v2)
Solution
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2F82ba6499-1d26-4625-b62f-6014bf46e819%2FUntitled.png%3Ftable%3Dblock%26id%3D3f33b332-d1f0-4688-9058-461a1813bdd7%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725789600000%26signature%3Db6C1TYVyIM2DdBDFqaFaKbfan167iNfXjzGAA62h0Qk?table=block&id=3f33b332-d1f0-4688-9058-461a1813bdd7&cache=v2)
Lab1 (A Minimisation Problem) Part B Q2: [!obj. function]
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2F81f81a28-5be8-43cc-a82d-8ef5829f89e6%2FUntitled.png%3Ftable%3Dblock%26id%3D97b4f831-be93-4ca7-8363-a2bb456799cd%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725789600000%26signature%3D-tWhZ3a8VOWVb3ow0ecmRSepviru3Nqx0zJIzDblfBw?table=block&id=97b4f831-be93-4ca7-8363-a2bb456799cd&cache=v2)
Solution
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2Fccb09e46-5766-4f59-831e-8e6b8d3321ea%2FUntitled.png%3Ftable%3Dblock%26id%3Da0b8b3d4-a5f5-4e79-ac07-d5091db4602f%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725789600000%26signature%3DVBnDBFt_fltp4eLKkj5UXbiBKpCkIUnlxuALw-ynG-8?table=block&id=a0b8b3d4-a5f5-4e79-ac07-d5091db4602f&cache=v2)
Lab1 Addtional Q2.6: Graphical
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2Fe326043e-ec75-4e87-9abc-d9f7b76860da%2FUntitled.png%3Ftable%3Dblock%26id%3Dcff0bf80-3ea6-4d7f-abe6-fe9e896a8b2e%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725789600000%26signature%3DdfZ4ScCqVdeQS-x_XI7r0WgTOutKBrk6LCHlFcSY74s?table=block&id=cff0bf80-3ea6-4d7f-abe6-fe9e896a8b2e&cache=v2)
Solution
Lab1 Additional Q2.7: Graphical
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2F6f9ae9a3-ebcb-42af-bece-4086b53b4f20%2FUntitled.png%3Ftable%3Dblock%26id%3Db2ef7deb-88af-4fcb-aeb9-77bab1298435%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725789600000%26signature%3DHAmKYTM4_76dvQSaRRA3zGHu-9eefzCEJtUsS_UZL2Y?table=block&id=b2ef7deb-88af-4fcb-aeb9-77bab1298435&cache=v2)
Solution
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2F9f795d43-771b-4e20-a7b0-3091d64ee35d%2FUntitled.png%3Ftable%3Dblock%26id%3D38248f40-b91a-4f38-8d96-638e7b2f0919%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725789600000%26signature%3DfOpw5CLAl0I3mrGNOPmFqojEKCUQYbLEesTpiSQJFWY?table=block&id=38248f40-b91a-4f38-8d96-638e7b2f0919&cache=v2)
Lab1 Additional Q2.8: Graphical
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2F2d0fd7b1-d15c-465f-adf1-f60cf20525b4%2FUntitled.png%3Ftable%3Dblock%26id%3Daa54e2b3-007e-4d8e-801d-6b3f4f1702e6%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725789600000%26signature%3DAhKDQ4hcLl_0v0_eBQsHDycHJa8iteE4jbIxkUbtofM?table=block&id=aa54e2b3-007e-4d8e-801d-6b3f4f1702e6&cache=v2)
Solution
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2F218d112f-ee28-47b7-8da7-b14cc68a6dfe%2FUntitled.png%3Ftable%3Dblock%26id%3D937a02f8-dcdb-4117-9ccb-8596f5cbb336%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725789600000%26signature%3DmPc3Tn3zR7IPEOn0BZhfPC7CBqYddUjU4YS95wvMDDA?table=block&id=937a02f8-dcdb-4117-9ccb-8596f5cbb336&cache=v2)
Lab1 Additional Q2.11: Graphical
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2F7a2791f7-c002-42aa-9ce5-1acfdd7555ea%2FUntitled.png%3Ftable%3Dblock%26id%3D8ff06eba-077d-4567-a953-30d2d79ebb8d%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725789600000%26signature%3DZp1Hr7AcpRxGMukTVu6n6hCAGQs9e8pZf29EUOkemSE?table=block&id=8ff06eba-077d-4567-a953-30d2d79ebb8d&cache=v2)
Solution
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2Fd62c0c50-1733-45a7-abc0-09b8dd5ce7d2%2FUntitled.png%3Ftable%3Dblock%26id%3D6213cb91-7f00-4254-9a55-acce831a3d5a%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725789600000%26signature%3DxdQZRl9Hx1LVUW0MlPPdCztMZLtv2UrMrXCl7nT337M?table=block&id=6213cb91-7f00-4254-9a55-acce831a3d5a&cache=v2)
Lab1 Additional Q2.13: [!EZ]
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2F3311144e-bd06-4d24-80b8-b3de73076853%2FUntitled.png%3Ftable%3Dblock%26id%3Da75ea118-18a8-464c-b190-135a95b03a9e%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725789600000%26signature%3Dl28zFhy2pP3KLF_hsEb0SP0u65m9y0_QEihRLRA6hAs?table=block&id=a75ea118-18a8-464c-b190-135a95b03a9e&cache=v2)
Solution
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2Fc0ffd905-3c96-47c7-a4f5-77864c9cb2b0%2FUntitled.png%3Ftable%3Dblock%26id%3Ddadc00d0-87e9-4ec8-b228-dfffb551f1d3%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725789600000%26signature%3DaQrNf7mwVQlsuKSopGiROEaW6UGnnHLd6wZSrlkFzRk?table=block&id=dadc00d0-87e9-4ec8-b228-dfffb551f1d3&cache=v2)
Lab1 Additional Q2.21: [!Difficult]
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2F11bf315c-24cd-4b10-b3dc-f5d8e6a420fe%2FUntitled.png%3Ftable%3Dblock%26id%3Dba36d9e1-321e-4b8d-8de7-7ec38f4072ab%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725789600000%26signature%3DlXi8uBT2LapSrdzPAL-MDD1KBLViBi25QPvX8j2tZe0?table=block&id=ba36d9e1-321e-4b8d-8de7-7ec38f4072ab&cache=v2)
Solution
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2Fe67b1a86-06d8-4f0d-917f-4bd6d819c13a%2FUntitled.png%3Ftable%3Dblock%26id%3Ddf2ab259-f9eb-47e1-9175-3c820a1c7a47%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725789600000%26signature%3DWr48PTFwjb0n9CvUZ_GtBxDCjFbChDTWg_ObQr20I10?table=block&id=df2ab259-f9eb-47e1-9175-3c820a1c7a47&cache=v2)
Lab1 Additional Q2.24:
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2Fa8fc2b04-55ff-4ba0-aab5-b61d68ac0e1f%2FUntitled.png%3Ftable%3Dblock%26id%3Dd1cca8f9-ed18-4388-aadd-d0f54b1425e5%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725789600000%26signature%3DvSfBs7_Yvv_bCo9iAQGr6unpA8s7mrq3jG47KnMLHYo?table=block&id=d1cca8f9-ed18-4388-aadd-d0f54b1425e5&cache=v2)
Solution
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2F01cff1f2-76b3-4bf3-8587-3d1171116ca8%2FUntitled.png%3Ftable%3Dblock%26id%3D9232a945-b312-4ecc-86b4-1b8d3162a702%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725789600000%26signature%3DpxfM3MAzmwaeOX7Z4t8ryjnj-28XYCWcDcGgtPdPW-E?table=block&id=9232a945-b312-4ecc-86b4-1b8d3162a702&cache=v2)
- Author:Jason Siu
- URL:https://jason-siu.com/article/cf306c52-73c4-493f-a0d8-9532e3d7b950
- Copyright:All articles in this blog, except for special statements, adopt BY-NC-SA agreement. Please indicate the source!
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