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Find the maximum value of C = 3x + 2y Subject to the following constraints: x ? 0 y ? 0 x + 3y ? 15 4x + y ? 16 Find the maximum value of C = 3x + 2y Subject to the following constraints: x ? 0 y ? 0 x + 3y ? 15 4x + y ? 16

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Elementary and Intermediate Algebra Alan S. Tussy, R. David Gustafson 5th Edition

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- Objective function: \( C = 3x + 2y \) - Constraints: \[ \begin{array}{l} x \geq 0 \\ y \geq 0 \\ x + 3y \leq 15 \\ 4x + y \leq 16 \\ \end{array} \] Show more…

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Transcript

00:01 Hello, i am a teacher for this question and our question says that find the maximum value of c equals to 3x plus 2y subject to the following constraints x greater than equal to 0, y greater than equal to 0 x plus 3 y less than equals to 15 4 x plus y then equal to 16 so how we're going to solve this question just say that find the maximum value of c equals to 3x plus 2y then and after subject to the following constraints x greater than equal to 0 y greater than equal to 0 then x plus 3 by less than equals to 15 and then and after 4x plus y less than equals to 16 all right so just say that 3x plus 2 y all right x plus 3 y is less than equals to 15 so i'll be writing that x plus 3 y less than equals to 15 can be written as as x by 15 plus y by 5 is less than equals to 1 all right so on x -axis this should be equal to 15 and on y -axis this should be equal to 5 so x is 15 y is 5 you will be writing here all right so after that what i will be writing ahead is that is that is x is 15 goma 0 and y is 0 .5 and you will be seeing that when i put 0 plus 0 less than equals to 1 so 0 is less than a question when i put the origin here it will be satisfying so the shading will be downside all right then after 4x plus y is less than equal to 16 can be written as x by 6 x by 4 plus y by 16 is less than equals to 1 so x by 4 plus y by 16 so on x xx is there will be a 4 and on y xx is just see that you can write this way all right 4 .0 0 16 and this is also satisfying the downward direction that 0 .0 so 0 plus 0 is less than equals 1 0 is less than a 1 so i'll be writing that this will be satisfying so this will be the feasible solution here and you will be finding this as 0 .0 this has 0 .5 4 .0 and we're going to simplify this both the equations. 02:49 Right simultaneously. 02:51 So i will be writing that 4x plus y is equal to 16 let's say and then x plus 3y is equals to 15. 03:05 Alright, so i will be writing that you will multiply the second equation by 4. 03:12 So 4x plus 4 312 by 15 4x and 4x plus y is equal to 16. 03:22 So subtract subtract and subtract and then subtract... Need help? Use Ace Ace is your personal tutor. It breaks down any question with clear steps so you can learn. Start Using Ace Ace is your personal tutor for learning Step-by-step explanations Instant summaries Summarize YouTube videos Understand textbook images or PDFs Study tools like quizzes and flashcards Listen to your notes as a podcast

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