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Andrea's Day Spa began to offer a relaxing aromatherapy treatment. The firm asks you how muchto charge to maximize profits. The first two columns in Table 10.5 provide the price and quantity for thedemand curve for treatments. The third column shows its total costs. For each level of output, calculate total revenue, marginal revenue, average cost, and marginal cost. What is the profit-maximizing level of output for the treatments and how much will the firm earn in orofits?

$\$ 80$

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So this question off, what soda? Andrea's Day Spa begins to offer a relaxing Armagh therapy treatment, and the firm wants you to acts different, actually out much to charge to minimum, to maximize profits on. We have a table that shows the price and quantity on the first two columns. We also have the third Column as a total cost. Basically, the question wants us to calculate the total revenue, marginal revenue, average, cost, imaginable cost and also the profit maximizing level of output. What the treatment and how much would the firm earned in profits? So I'll be drawn the table, which shows the price, quantity and the total cost. I will just find the rest of the question with the same table. So So basically, for this question, what to find, um, the total revenue, the marginal revenue, the average cost and imagine our costs and also the profits. So that for us was a fine for this question. So we'll start by drawing the table that shows the price and the quantity. So Okay, so the price for the first for the price we have 25 we have 24. We have to ring three 22.5. We have 22 21.6 on 21.2. So that's that's so we also have the quantity. The conference is zero chain 20 on Thurdsay, trying to joy life. So it doesn't, um you can tell the difference between them. Yeah, okay. We have to see we have 40. We are 50 on 60. Also giving to our cost. The question I know. I just keeps joy. Also give me total cost as one third c So 75 4, 35 6, 10, 800 1000 and five and 1000 su 25. So the first part of the question was was to find is the total revenue. Yeah, total revenue. So so, ceremony, which is CR? We know that the formula for finding total revenue is p times Q, which surprised times quantity. So go over here and say the formula for finding revenue because revenue is like how much you hand. So the price you sold time to constitute you sold, so that's totally riveting. So the terrain is p times Q. So we go back to the question we see p and we seek you So basically, we multiply the P and Q for each line. So 25 times zero is zero. 25 times 10 is to foresee. So the next line 23 times 20? Yes. Um 4. 60. So we're for six over there, then the next one is 6 75 and we have 88 C 1000 and eight c and they 1272. So the next thing the question was, was fine is marginal revenue. So we draw the line for imaginary renew. I'm sorry, my life. I love that streets so we don't have the formula for marginal revenue is total revenue tu minus two tax revenue? One divided by it saying so. That means the first one will have noted imaginary revenue. The second line. The second column. No rather role. We'll have. Imagine how revenue off the total revenue, minus just a revenue of one developed by 10. So that's 2 40 minus zero, divided by 10 to 14.2 40 divided by 10 24. The next one will be 64 60 minus 2 40 divided by 10 so that we have 2 20 to develop by 10. That's 22. The difference in this is 1 2050. No, did that's going to be 1 2050? Yeah, they divided about If we divided by 10. 21.5. The next one is 20.5. So once you have the formula, basically is easy to do and this is 20 and then this is 19 points to the next thing the question wants us to find is the average cost. So a C average cost is the formula for average closed. I'm going to write you value. I'm all for average courses. Total cost divided by quantity. So we'll go back to the question to tell cause divided by quantity. We have the cost over here. The total cost, which is this I wanna buy quantity so wanted to do better by, um, zero is not that survived by zero is zero because anything the advisory zero. So that's the then on 2. 75. Better by 10 is 27.5 on 14th. Father will buy 20 21.75 The next one is 20 points. That's a three we have. The next one is 20 The next one is 20 points one and then 1000 to 25. Whatever 60 is 20.42. So that's that's the next question was justifying the marginal cost. So we're gonna right into phone off of marginal cost from her from marginal costs is total cost to minus 2000. Cost one developed by saying so. We're gonna have marginal costa by you. Marginal cost. So total cost. One talk was to minus total cost. One is better by 10. So the first on the B zero, obviously, to that cost Sumana start cost one is to 75 finals wanted, See developed by chain. We have 14 points. Five. The next question is 16. The next one is 17.5. Then the next one is night. Seeing the next one is 20.5. The next one is 22. So for desk for that desk, that's on. The next question was justified the profits. So I'm going to find the profits also right. Jesus, Profit. So for the profits, the former for profits going down here honestly, just outside the formula and you're good. The former for perfect is the total revenue minus two South coast. Because preferences what? You and minus watches Spain. So ever. If you're gaining more than he spent, the rest is always a profit. So that's it. So total revenue minus total cost. So tr minus D. C for this zero minus wanted his minus wanted. See 22 40 minus 2 75. Oh, total cost my nurse today of any minister del cost. So we look at this. The ceremony minus two dark cost the profits or this is minus 35. Next one is 25. The next one is 6 to 5. Next one is 80. The next one is 75 on the next one is 47. So that's that. That's the prophet I remember. The question also said, um, what is the profit maximizing level of output? We found that on how much with the firm and in profit, So we found the profit. So that's finding maximization. So if you go back to the question, we can say that when when they're 40 treatments provided by the frame, the prophet is maximum. The prophet is maximum at $80. So if you check the $80 a year, that's when we have 40 treatment. So this is where the profit is maximum because the prophet is obviously maximum at $80. So the trees 82 the quantity we have 40 treatment is provided by the firm when the firm is at maximum, if that makes sense. So we're going to say the firm provides Fort C treatment when the profits is at its maximum, which is $80 and that's the answer, that question.

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