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Problem 70

Time In Exercise 39 of Section $9.3,$ we saw that…

03:34
Problem 69

Average Revenue A company sells two products. The demand functions of the products are given by
$q_{1}=300-2 p_{1} \quad$ and $\quad q_{2}=500-1.2 p_{2}$
where $q_{1}$ units of the first product are demanded at price $p_{1}$ and $q_{2}$ units of the second product are demanded at price $p_{2}$ . The total revenue will be given by
$R=q_{1} p_{1}+q_{2} p_{2}$
Find the average revenue if the price $p_{1}$ varies from $\$ 25$ to $\$ 50$ and the price $p_{2}$ varies from $\$ 50$ to $\$ 75 .$ (Hint: Refer to Exercises $61-64 . )$

Answer

$\$ 34,833$



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Video Transcript

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Um uh then interval rate with respect to be too dp to we're happy to Is the price off the king product? So far, so good. This is good too. We get here. We're, like over a 625. Yes, injury grew 50 from 52. 75 Then if we pour the vory v p here on, put 25 Here we put so 50 on DDE 25 15 25 You were good. We have 115 then times 50 squared is 215 2500. 1250 Didn't mind us or 25 spread Just go to minus 600 25. So I'm in a good position. Yeah, Then minus to aura told divides by three then here we have. We're going to put the very 50 25 here and pick you, which is Goto 50. P Cube would put 50 Cube, my ass. 25 cube. Here's to you. My last 25 cube. It used my ass here. There is most pissed. So means that they can arise here. Yeah, So our average reading you. Hey, uh, condom be good too. Let me repeat this world because there's no space here. I can't Even Your Grace, it's here. And then they do. Yeah, it's gonna be curious. So this is a warn over sorry or 360 hundreds. 25 on over 625. So, having table from 50 toe 75. So if we put the body off or P one here, this is good. Too. 115 under than 50 times. 27. 50. Scratch my nose. 25 screams. 50. Scared my last 25 square. Yes. And then we're gonna report very off. Be one horse. Here is this minus tool my ass to over three. Asked to grow from three times, he'll have 50 cube 50 cube, 50 cubed, minus 25 cube, 25 2.3. Yes, I have to be very sport. Our double 25 then Cuba Here, then press here. Are you here? Up? He would have calculated up to here on dhe prayers. 500 time Z 50 minus 25. A proponent of my last lower browned. This is very off p weren times p too. Then minus one point tool Titans 2015 minus 25 which is go to 25 Peter de nuit crawlers. This crypt square brackets then d y we can do. Then we can continue if intramural directing with respect toe. So that here we calculate there are you after? So this is good too. If Rick or even this constant. This is 50 square on my last 25 sprayer. So have to regret this. And we have took a great piece because this is no independent. Ah, there is no pure no p to This can't be you Goto or kill Benny called this constant a small a So with the integrated, this one would have a diamond sippy Because thymus Peter is not depend on did. This is constant Not depend on Peter. So very rabbinical toe warning or it's had tried to have enough space to use this piece with her. We have a one over three hundreds. 25 but not 300. But 60 100 25 this value, then time. See, we have eight times p too. Because we are going to integrate with respect to Pito. Not why? Sorry. P two. Yeah. We're going to injure grates with respect to Peter means that this is constant. We have to Yeah. Then press, remember that this is 25 15 minus 25. 25 is 500 time was 25 soar over too. Because this is a peace. Peace. Andrew Grove P two is P two square over to So we're creating this one. This is go toe to 50. You're 15 2 50 times e 25 Peter Peter screen. Remember that Tear off Pete tours with respect to pee too is Peter's square Over to then a 500 off two is 52 is 250 59 hours 25 This is 25. This is correct Then minus I think he overheard of peace. Creer Yes, we have peace. Chri Yes. You have peace Clear here so King would have peace clear over a city piece. Gray of precedent is that it's pee. Too poor to press. One is P Cube. Pito Cube. This is pee Tube. Event is, um if you're SP too. Yes, Peter Cube. Peter Cube. Over three. This is good to throw 24 because the one point toe Dorothy Time Z 25 he took you. Then we put for your 75 and 25 not 50. This is good too. Hundreds, not 100 1 of us 625. Remember that we have so current rate this one A by no program and corner creatives. But here we heard a time Z 75. My last 50 here means that's his 25 a 25 a. Your car gets very off, eh? There were about death. So here we have 75 minus 75 square minus 50 scream. So this sorbet good through here? 50 we have. Okay. Well, do they card? Question. We've We've come together after him. Right? 50 time was 25 Ben time Z 75 square minus 25. Screen don't mind us. 0.4 times 25. 25 times for his 100 seances. 10 minus 10. Then we have 2075 cube. So when five cube miners 50 cube our care Now we have ever think what we are going to do is to use the curricula. Thank you. Create this for you. This one. This one on Get the answer. Jamie was premios carrick it and find this solution. And it would have to do some simplification bringing 625 so Oh, ah, our average or even you. Our eight are forgeries in you forever. Egidio breathing you? It's good to yeah. 150 50 square, minus 25 Got cancer. You see him? I give something here and in here and left tackle creating for those We get 10 calls and and 500 over three. God knows you're Greta and you get this is good too. Three. Yeah, A three, three point three three three. Those are Charles and doors. So this is the answer. This is the average oration. You? Our average revenue is 34. Charles seemed HR under that through three