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Marginal revenue Is the derivative of the revenue function; s0 and evaluate it at x = 100: take the derivative & R(x)Thus, the approximate revenue from selling ...

Question

Marginal revenue Is the derivative of the revenue function; s0 and evaluate it at x = 100: take the derivative & R(x)Thus, the approximate revenue from selling the 101st part is $Profit, P(x) , equals revenue minus costs P(x) R(x) C(x)Marginal prolit is the derivalive 0f Ihe profit function SO take the derwalive of P(x) and evaluate it al X 100.So; sellling the 101s/ par brings in an approximate prolit 0l By Ihe way; whilo Ihe above math exacily whal you d want I0 do you were asked only to c

Marginal revenue Is the derivative of the revenue function; s0 and evaluate it at x = 100: take the derivative & R(x) Thus, the approximate revenue from selling the 101st part is $ Profit, P(x) , equals revenue minus costs P(x) R(x) C(x) Marginal prolit is the derivalive 0f Ihe profit function SO take the derwalive of P(x) and evaluate it al X 100. So; sellling the 101s/ par brings in an approximate prolit 0l By Ihe way; whilo Ihe above math exacily whal you d want I0 do you were asked only to compute Ihe marginal profit; did you nolice Ihal il was unnecessary in this Once you know Ihe margina cost and Ihe margina enue; you can g8l example? marginal profit F with the following simple (ormula: Marginal Profil Marginal Revenue Marginal Cosi



Answers

Marginal revenue, cost, and profit. Let $R(x), C(x),$ and $P(x)$ be, respectively, the revenue, cost, and profit, in dollars, Irom the production and sale of $x$ items. If $R(x)=5 x$ and $C(x)=0.001 x^{2}+1.2 x+60$ find each of the following. a) $P(x)$ b) $R(100), C(100),$ and $P(100)$ c) $R^{\prime}(x), C^{\prime}(x),$ and $P^{\prime}(x)$ d) $R^{\prime}(100), C^{\prime}(100),$ and $P^{\prime}(100)$ e) Describe in words the meaning of each quantity in parts (b) and (d).

The perfect function. People will river. When does the post the marginal? He's, uh so fine. So what That means. But the marginal revenue means is, uh, how much is gonna cost you two brothers? One more. One more item. How much more than you will get for bruising? One more item. So it's kind of like a discreet there you have living, you know, it's one. What is the difference on the revenue If you Well, because you're Explorer one. So will they. Moxie, more profit. Much profit will occur because that, uh, I'm just brought it being a what? The perfect. Having zero. She did. It does there the zero. Is that our Brian? What is this, right? She was here. Does you need that? The marginal rather than is equal to marginal cost. Um so in particular. So this is Bert. You have a question. So I'm particularly if you have the following cost function close to live in the next people toe six poses minus 500 looks minus one point six squirt plus point. Oh four. Is the cost function there have any function? You see goto sitting hard goods nexus X um, minus seven. X squared. Also, you know, better profitable. Who marks for marginal word being ableto marginal cost. So you go ahead. I'm fine. What is the marginal cost? So your friendship This? Oh, all the everything. That's so you have Ah, 500 minus. Do the damn swamp. 16 rise from six from six on marginal people. So seven hundreds, Uh, minus 14 x or that's so those two are equal. When you have well in here to burn on top two, you're gonna get under minus three for two. Looks should be able to hobbits wires working X So you know these guys there? 500 move or Keane looks to decide. What would you get? You're not getting one of you. So over decide 14 minus 3.2. The tense X should be hope too. 1700 minus five. I know that this gives you well, 10 on age. Thanks. The she goat. So these would be just so it's so your ex should be people for hundreds buried by and which is a rough something of the only It'll be glares with No, you're done. 1 19 So these were to give you marks the moment forbade x You're gonna have the maximum Brooke

Profit is defined as the revenue minus the cost. So if we wanted to find the maximum profit, we would want to take the first derivative of the prophet function and set it equal to zero so we can do this and pieces would say it's equal to our prime minus c prime and set that equal to zero. So that tells us that the first derivative of the revenue function would equal the first derivative of the cost function. And it turns out that is the marginal revenue function. And this is the marginal cost function. So these two things are equal to each other for the X that maximizes our profit.

Yeah. Okay. The Prophet is the revenue minus the cost. So in part a the profit it's a function of X. Is revenue minus cost? That would be 50 x minus 0.5 X squared. That's the revenue minus four X minus 10. That would be subtracting the cost. Just rearranging this negative 0.5 X squared. Then combining like terms 50 minus four is 46 minus 10. Okay, so that's the profit. B mm was the revenue cost and profit for 20. So the revenue at 20 is 50 times 20 minus 0.5 times 20 squared the cost at 20 his four times 20. Yeah. Four times 20 plus 10. Well that's easy. Four times 20 is 80 plus 10 is 90 first one. I'm going to have to use a calculator. So I'm going to dez most dot com graphing calculator 50 times 20 minus 0.5 times 20 squared eight $100. So the Prophet would be revenue minus cost, 800 minus 90 is 810. Yeah. Okay let's see what we got to do next. Find the derivative of everything. So derivative of the revenue would be negative 0.5 times two negative 0.5 times two. Which would just be negative one X plus 50. We just took the derivative fruit of the cost would just before drew to The Prophet which is revenue minus cost would be negative X plus 46. And now I just need to do the derivative at 20. So negative 20 plus 50 is 30 and this would be dollars per item. See prime of X would be $4 p. Prime of 20 negative 20 plus 46 which would be $26 per item. That's it. Thank you for watching.


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