Linear Programming

This precalculus video tutorial provides a basic introduction into linear programming. It explains how to write the objective function and constraints of linear programming word problems. It discusses how to find all of the corner points including the point of intersection where you have to solve the system of linear inequalities. It discusses which region to shade and how to determine the maximum profit or sales produced by a company or business and how to determine the number of items that should be produced to maximize such profit or revenue. This video contains plenty of examples and practice problems on linear programming.
Systems of Linear Equations - 2 Variables:
• Solving Systems of Equ...
Systems of Equations - Fractions & Decimals:
• Solving Systems of Equ...
One Solution, No Solution or Many Solutions?
• One Solution, No Solut...
Systems of Equations - Substitution Method:
• How To Solve Linear Sy...
Solving Systems of Equations By Graphing:
• Solving Systems of Equ...
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Systems of Linear Equations - 3 Variables:
• Solving Systems of Equ...
Systems of Equations - Word Problems:
• Algebra 2 Math Problem
Systems of Quadratic Equations:
• Systems of Quadratic E...
Systems of Nonlinear Equations:
• How To Solve Systems o...
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[@TheOrganicChemistryTutor]

Final Exams and Video Playlists: www.video-tutor.net/ Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections Next Video: kzbin.info/www/bejne/r4Pagmp3a8-Jgs0

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In this video, when you were calculating the intercept why did you use -9 to calculate the first constraint?

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[@muhammadhaziq3787]

why is on 28:41 , why we have to *-9, where does the -9 come from?? can someone explain to me?

[@perezfono2092]

@@muhammadhaziq3787 -9 is used for the elimination method of the two equation by multiplying first equation by -9 in order for us to eliminate R and calculate T

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why is on 28:41 , why we have to *-9, where does the -9 come from?? can someone explain to me?

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[@Bill-xv9mz]

Excellent video, as are all of your videos. The only changes that I would make for problem #1 is to incorporate the cost into the objective function [(20-5)B + (18-4)C = 15B + 14C], and to round down the calculator figure to 1472 (since you cannot produce more than 1472.73 calculators). Explanation and presentation was excellent and very straightforward, much appreciated!

[@nel3960]

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yes, you're supposed to round down

[@masterdementer]

I was thinking the same thing. But then again we are rounding down the books as well. So we can choose to round one of the two to upwards as long as the end values we get do not break the inequality. If we put in the values of C=1473 and B=4221. We get 26997

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[@frederickdvorak6502]

For books and calculators: Good approach, although the objective is to maximise profit, not sales (which you end up doing, but the long way). (1) Possible improvements: (a) Objective: MAX[Profit] = MAX[B*(20 -5) + C*(18-4) = B*15 + C*14] will get you to the answer faster in your table. (b) Always round down any number of item produced to the nearest unit you come across. If you consider continuous production, leave the decimals because the fraction not produced in one month is picked up by the next month. That said, the practice is to round down for each period. (c) Calculate for 28, 29, 30 and 31-day months. (2) Your conclusions on profit (and also number of items) are incorrect: (a) Using your numbers: Total costs = 4,221*5 + 1,473*4 = 26,997, not 27,000 (27,000 is the maximum limit allowed, not the maximum imposed). Thus, profit = 83,937 (not 83,934). (b) If the optimum solution requires rounding down the number of calculators to 1,472, this liberates a few minutes that can be used to produce 1 extra book, whilst still satisfying the time and maximum cost constraints. Thus, maximum profit = 83,938, achieved with: 4,222 books + 1,472 calculators; 43,190 minutes of production; total costs of 26,998; sales of 110,936 and cost of 26,998.

[@rhodaime79]

Total agree with you about the objective function. I used B*15 + C*14

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[@muhammadhaziq3787]

why is on 28:41 , why we have to *-9, where does the -9 come from?? can someone explain to me?

[@daveryan941]

Thank you so much I finally understand linear programming and I think I can actually do it well for my exam tomorrow.

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[@muhammadhaziq3787]

why is on 28:41 , why we have to *-9, where does the -9 come from?? can someone explain to me?

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[@NemoN0body]

nice video, i think a small correction you should make is to incorporate the cost into your calculations while doing them, because sometimes you are constraint by the time and not by the cost, you get the right number of units to make but you are calculating the profit wrong, for example 2 you are making 20 tables which cost you in total 300$ and not 315$ (20*15), so you're profit is 1500$ and not 1485$, this would have been avoided if you had (T75 + R135) for profit calculation. also another thing with exercise one, it wasn't clear if we are using the same machine for both books and calculators (logically that wouldn't make sense for obvious reasons) but we solve it assuming that is the case.

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[@maxma2194]

Excellent video! However, I noticed that for the books and calculators question, 4222 books & 1472 calculators is the optimal solution, giving a profit of $83938 instead of the $83934 in the video (which itself should be $83937 based on the correct formula). Explanation below: This is because we need to consider the objective function as maximising profit, not sales. This gives P(B,C) = (20-5) B + (18-4) C = 15B + 14C , which returns the correct answer of 4222 books & 1472 calculators. Hope this helps! If I'm wrong, please feel free to correct me :)

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