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:

Systems of Equations - Fractions & Decimals:

One Solution, No Solution or Many Solutions?

Systems of Equations - Substitution Method:

Solving Systems of Equations By Graphing:

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Systems of Linear Equations - 3 Variables:

Systems of Equations - Word Problems:

Systems of Quadratic Equations:

Systems of Nonlinear Equations:

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Final Exams and Video Playlists:

Full-Length Videos and Worksheets:

[nymphaea]

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[eugenioblanco]

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[chifuyumatsuno]

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[miowooshawn]

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[davibeats]

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[tam]

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[Bill-xvmz]

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!

[bugra]

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[courtneytroup]

I love how much simpler this is compared to my teachers explaining it. Funny since they spent a whole unit over explaining PEMDAS and other basic algebra so it's not like they don't know how to explain it. But as soon as we get to new info they just glide threw it. Even when doing examples the explanations make no sense and the lecturer just mumbles through them 🤦‍♀️😒 I was about ready to rip my hair out, so thank you for this

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[jacoblee]

you’ve got a gift, two well paid professors couldn’t convey this concept as clearly as you have. Thanks!

[shirousensei]

If only our math teacher provided us with videos like this, I could've passed the all of the exams.

[adabuilder]

Thank you so so much!!! Linear programing is 30% of my grade and I was not understanding the professor's lecture at all! You explained it so well!

[unconventionalgriffin]

You sir, are a lifesaver. I was having trouble understanding this concept in my Algebra 2 class, but you explained it better in 30 minutes than my teacher could in over an hour.

I have a test on this in a hour...let's hope this goes well :/

[xav]

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[frederickdvorak]

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.

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[daveryan]

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

[olagokeoladapo]

Thank you very much for this, got Advanced Numerical Methods II examination for my Masters Program today, and this video cleared the linear programming aspect of it. I'll go attempt the assignment now having solved your second question on my own before watching the rest of the video.

[sparklinglilsecret]

THANK YOU SO MUCH for this now I can say I can do word problems of linear programming 🥀 Much love from Tanzania 🇹🇿