Optimization: profit | Applications of derivatives | AP Calculus AB | Khan Academy
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- čas přidán 30. 01. 2013
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Who knows, you may end up running a shoe factory one day. So it might not be a bad idea to know how to maximize profits. Created by Sal Khan.
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![How to Solve ANY Optimization Problem [Calc 1]](http://i.ytimg.com/vi/cUMvwG7wvzM/mqdefault.jpg)
Khan Academy flexing on us with that artwork
The only math teacher that knows how to draw
If you're looking for the question, here you go! :)
You own a shoe factory and want to figure out how many thousands of pairs of shoes to produce in order to optimize your profit. Let x equals to thousands of pairs of shoes produced. Assume revenue as a function of x. You know a wholesaler who is willing to pay $10 per pair as for many pairs you produce. The consultants you hired had come up with the cost in a form of function of x, which is C(x) = x^3-〖6x〗^2+15x. Given the revenue and the cost, what is the profit you can obtain?
why Price != Marginal Cost in this case?
if i hired a bunch of consultants why do i have to maximize the profit myself
Vera Lei so that you know you're not being cheated + this is VERY basic knowledge
What if you weren't in the position to hire people for you and YOU had to do these calculations for someone else?
Vera Lei Bcuz this appeared in my calc quiz.
We never even discussed how to do any of this at all
@@lifesimulator3964 Its on my final, so im here crying
@@lifesimulator3964 You determine the costs based on statistical analysis. You want to basically plug-in points into a machine and try to find a function based on what you have. The beauty of statistics.
@9:40 I don't know why, but I almost spit my food out laughing at this
Cool, this is similar to what I did in school this past semester, and it is very useful!
And in an actual setting how would you derive the cost function? Usually in business (furniture business) seems like more = always better
x increases from .4725 to 3.528; x decreases 3.528 to infinity. in this case, concave downwards means increase-max-decrease. it does not mean that slope is constantly decreasing. that would mean there is no critical point because the slope never flattens out.
8:20 I’m an Economist and while I appreciate the math I learned and much of it points to the right intuition, there is almost never a cost function nor a production function or any of that stuff. We went into pretty heavy math with differential equations, Hessians, Jacobians and lots of stuff I don’t even remember that well, but with very little practical,use. Mot so Econometrics, which should receive a lot more emphasis.
That shoes look fire
Studying for my exams lol...
Thanks alot for the help
Thanks for your insightful videos. Explained from the basics, these are very good and helpful.
But how to find which group of videos this belongs to ? Also I am not able to find the order I should follow.
I imagine the cost is the relationship between wages, equipment run-time costs, shipping, stocking, taxes, marketing, loans (if needed), and various other miscellaneous overhead expenses.
Excel probably has a spreadsheet for it.
How do you get cost function ? Or how do you make a cost function
what app do u use to record the screen and audio?
I'm enamored with this. I had the pleasure of reading something similar, and I was truly enamored. "The Art of Saying No: Mastering Boundaries for a Fulfilling Life" by Samuel Dawn
khan saving me yet again
🎉🎉🎉as always Khan comes through as our professor❤
Can you explain the cost function and where the numbers/variables came from ?
The statement is given, there is no necessary statement but the profit formula must be necessary.
where is the question?
Can somebody tell why Price != Marginal Cost in this case?
where 6 and 15 come from are those arbitrary numbers?
can you explain why?
Your diagrams are gorgeous, have you considered teaching arts?
A Mr. Peterson wants to sell cheese.After a fixed set-up cost of $250,
he can produce the cheese at a cost of $9 per kilogram.He is able to
produce up to 400kg,but he plans to take advance orders and
produce only what he can sell.His market research suggests that the
amount he would be able to sell depends on the price in the following
way:thea mount decreases proportionally with the price;if he
charged $20 per kg he would not sell any,and if the cheese was free
he would ‘sell’ the maximum 400kg that he could produce.What
price per kilogram should the farmer set in order to maximize his
profit?
dividing the profit function by x doesn't help us to find the point at which the maximum occurs . . .
dad34089 It's not dividing. It's deriving.
It shows the slopes, which determine if the profit's increasing/decreasing.
Crazy question here, but when you inverse a profit function like this and if you input an input greater than the maximum profit, you would need to sell an imaginary number of units. Isn't that just crazy? Or is that just plainly obvious and or wrong?
"We are now going to be rich shoe manufacturers"
Tom and jarre
How did the consultants come about the Cost function? I mean... This is just not helpful for applying in real life if you don't know how to model equations.
I think that you are only targeting business owners how have mathematical degree.
I'm pretty sure that was just a random function Sal made up.
Making the most profit for -ve x values, check the graph 😂😂😂
Tolong dong terjemahkan ke bahasa Indonesia 😭
My uncle owns a shoe factory.
dirac17 There was also a shoe factory in Valenzuela, Philippines.
It burned down.
300 people were trapped inside.
Burned alive.
Very painful death...