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OSAThe total revenue (in hundreds of dollars) from the sale of spas and solar heaters approximated by R(x,y) -1Sx2 21xY 507x 21y2 546y Find the critical points and ...

Question

OSAThe total revenue (in hundreds of dollars) from the sale of spas and solar heaters approximated by R(x,y) -1Sx2 21xY 507x 21y2 546y Find the critical points and use the second derivative test to find the number of spas ad solar heaters that should be produced and sold to maximize revenue: Find the maximum revenue.Select one: The critical points are: (x,y)-(11,8) At the critical point D-819 (positive) and R {X}=-30 (negative) and therefore the revenue maximum when *=11 and v-8, The maximum rev

OSA The total revenue (in hundreds of dollars) from the sale of spas and solar heaters approximated by R(x,y) -1Sx2 21xY 507x 21y2 546y Find the critical points and use the second derivative test to find the number of spas ad solar heaters that should be produced and sold to maximize revenue: Find the maximum revenue. Select one: The critical points are: (x,y)-(11,8) At the critical point D-819 (positive) and R {X}=-30 (negative) and therefore the revenue maximum when *=11 and v-8, The maximum revenue Is R(11,8)-4983 dollars The critical points are: (x,y)-(7,12) At the critical point D-819 (positive) and R_{xx} =-30 (negative) and therefore the revenue is maximum when x-7 and Y=12. The maximum revenue Is R(7,12)-4623 dollars The critical points are: (x,Y)-(10,8) At the critical point D=819 (positive) and {xx}=-30 (negative) and therefore the revenue Is maximum when x=10 and y-8. The maximum revenue is R(10,8)=4959 dollars d. The critical points are: (x,y)-(12,7) At the critical polnt D-819 (positive) and R_{xx} =-30 (negatlve) and therefore the revenue is maximum when *=12 and Y-7. The maximum revenue is R(12,7)-4998 dollars



Answers

Revenue The total revenue (in hundreds of dollars) from the sale of $x$ spas and $y$ solar heaters is approximated by
$R(x, y)=15+169 x+182 y-5 x^{2}-7 y^{2}-7 x y$
Find the number of each that should be sold to produce maximum revenue. Find the maximum revenue.

Given the total have a new function from the sale off expose and why? Sel sel Writers, we have to find number of reach that has to be sold. Produce maximum revenue. So with a different chick, huh? Aspecto different. You are partially with respect to eggs So 1 69 minus the next minus seven. Why similarly will differentiate are partially with respect. Why we get 180 Do my nose 14 Why minus seven x so really quit each of these partial that is reduced to zero No, no, don't find the critical points so this can be Do you recognise the next place? Seven by minus 160 Light is equal to you but can build nests then express seven y is equal to 1 69 Similarly, we can diet he says seven x bless 100 mean 14 by minus one A little secret a zero So that candidness Acquittal 182 I will saw things to equation in Question one Immigration to find out Critical points seven Multiply the equation one I do have subtracted with the ignition drawers Were this was one will become in question one will become 20 x less for by sick welcome. We kind of did to really question door. All right, Does this seven x plus 14 way Sequent 182. So now we'll subtract these two equation. So I will have 30 necks. They went toe 1 56 Check lies X is equal to 12. So shooting this you know the question Get white. Is it rectal 1 69 minus 10 x by seven It's nothing that why in the rental seven of critical point is 7 25 extra We will use the best We're finding dis commute. They just given this case? Yes, her ex eggs off. Welcome, I seven Duke Art. Why way off? Welcome on seven minus Uh, x y oaf. Well, come on. Seven was great for us. Calculate it, our execs Different shading are X With respect to X, you get minus 10. Similarly, our why right? Differentiating are tracked by partially I live right Different shooting our way with respect. Why will get minus 14 on our X y differentiating biotics within aspecto Why partially minus seven This sorely so constant. So we would just so certainly in question. So our xx soft Welcome on seven will be my nest in in tow are my way off. Welcome, I seven with minus 14. Mine is old. Are X Y is minus seven Scratch that is going to be 91. Good. And you also What is ego reading? That's more than a Dimino Our execs really? Come on! Seven Sequent Top minus 10. Which is this That Seattle in place are Miss Italy to maximum when X is a quinto. Right? And why is it Quinto seven Now we'll cancel it. The maximum Whatever new this got off trend. Come out. Seven that is given by the question 15 Bless Holiday 69 s that just tonight. 2028 less. 182. Why? For this 1000 to 74 minus five x cram at 7 20 when a sudden why square minus seven X way 518. And this is equal to Carson. 666. So this is given hundreds of 1000 hundreds of dollars. So it's going to be

What questions were indeed, uh, given the art of the clerk computer firm, uh, markets. Two kinds of calculators, even and P two other price of those calculators, while Cuban and Q two other types of the calculators and party we gotta find the revenue functions so revenue function would be there price times quantity. So that will be given Cuban. Plus, we took you to Let's Substitute Q one and Q two over here and multiply with Even so, we have 78 p one minus six. Be one square minus three p one p two plus 66 b two minus three b one B two, minus six b two square If you simplify this further, we have 78 be one plus 66 p to minus six p. One square minus six B, two square minus six B one p two. So this is the revenue function, which depends on P one as well as speed. This is part A and part B. We gotta find the prices which will maximize the revenue. So we find are the one that is differentiating the complete equation with respect the P one. So we have 78 y P Tuesday is treated as a concert. So this is what will have an r p one on. We do the same procedure with P two so R p two would be 66 minus 12 p to minus six. B one. They quit both these 2 to 0. So we have 78 minus 12, even minus six. No, uh, P two is equal to zero. Let's divide both sides by six. So we have 13. Uh, maybe we can write 13 on the other side of the equation. So we have two p one plus p two was 13. The CIS look squalid equation one on if he quit this to zero as in 66 minus 12 p to minus six p. 10 This means that if you divide both sides were six again. So we have to be two plus p one as 11. Let's call it equation toe from equation one. We have the value off be, too, in terms off, even as 13 minus to be one. We substituted that over here, so we have two times 13 minus two B one plus B one is equal to 11. This is 26 minus three. P one is equal to 11, which means that three p one is 15, which means that the one is five. This is the value of P one, and let's substitute even over here. So we have P two as 30 my understand, which is just three. So the critical point is, uh, three and five is five and three on. Since this is the only critical point, there's no there's no significance off finding whether it has a local maximum minimum because there is only critical point and we're asking about maximizing. So it has to be the maximum eso these other two final answers for Cuban and Cuban in part C. We're supposed to find the quantity so Cuban would be replaced the values of P one and P two years. So P one is five will be to us three. So we have 78 minus 30 minus nine. So this week amount is 78 minus 39 which is nothing about 39. So this was the quantity off calculator cube one on. If you talk about you toe exactly the same procedure because we got a substitute these over here, so it will, it will be 66 minus three p one. Again, the one has five minus six p two Y p tours, three sort of 66 minus 15 minus 18, which is nothing but 66 minus 23 66 minus 33 which comes out as 33. So that's a skewed to which Waas asked on. The last point is, they're asking about the maximum revenue. So we're supposed to find the value of R P. One p two. So from here we take the equation, the function for our even p two. It's over here and we substitute P one and P two. So we have our even be, too as 78 the one where he even is. Let's write it again in the side, even as five and we two is three, so we have 78. In fact, there is no point of going in that details because we already have even Cuban P to Q two. So let's do it even Cuban plus p. Tokyo to because we already have all these four. We one is five you one is 39. B two is three. Q two is 33 So if you simplify this, we have 39 times five. We have 39 times five is 1 95 and 33 times three is 1990. We are both. We have the final answer as the final revenue in factors to 94. And since this is to the thousands, so we'll add 1000 over here. So this is the final or maximum revenue. And since the prices into the nearest 10, so we can say that this is the value of people in P two. But the price would be price. P one would be 5 50 on the prize. P two would be 30. This is what we can right here. And the quantity is to the nearest 100. So we'll say the quantity Cuban will be 3900 units on quantity. Q two will be 3300 units. That's shift a little bit of what down. So we have que tu as 3300 units. So these are the actual units. While he wanted you toe for the sake of putting in the equation. So all these would be our final on cells

And everyone. So working with the function are fats is equal to negative. 60 at squared plus 300 EDS On it represents the mutton. Well, the equation for the revenue 30 company makes for some for its movies, and we have to find the maximum value of revenue. Okay, so the first thing we gotta do is take the derivative of this function. So our family fats the sequel to Negative 1 20 That's plus 300. Now we're gonna equal. This is true. So we have 200 these people to want Donets. Basically, I just moved a negative 1 20 ants to the right by adding 110 yet to both sides. Now we have to divide by one training. So 300 divided by 1 20 he's able to ads. So that's the sequel to Are You Retell 12 which is equal to 15 over sets. Uh, this is a marksman price per item that's coming maximizes the revenue. Now we have to pluck this in to the renal function. So we have our 15 over sits 15 over sets, the sequel to negative sits T 15 over sits square 1st 300 times 15 over sits, uh, you complacent to your calculator and get the results. So I'm gonna do that, and then I'm gonna tell you the results. So the number that I got waas 300 looks 300 on 75. So that means that if the company sells Moody's for $2.50 $2.50 then it's gonna make a revenue off 200 and $75 and that is your answer.

For the given problem, we have the revenue and the cost function. Um So we're going to go back to what our revenue and cost functions are. Um We have a revenue function of X Times 2000 yeah minus 60 X. And then see if x equals 4000. Yeah, That's 500 x. So this is the result thing graph. Um And we see that the X intercepts of the Prophet function are ultimately going to end up being the same as the X intercepts of the break even points. These are the same X intercepts if you remember from the previous problem, because this is the same cost and revenue function. However, what we see is that the Prophet, the maximum that occurs is not going to be the same as the maximum revenue despite popular opinion.


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