Posted: 3/23/2013 6:28:44 PM EDT
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John owns a hotdog stand. He has found that his profit is represented by the equation P(x) = -x² + 60x + 71 with P being profits and x the number of hotdogs sold. How many hotdogs must he sell to earn the most profit?
20 hotdogs 31 hotdogs 41 hotdogs 30 hotdogs |
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Correct answer is 30 hotdogs... I got it wrong  How can he make more profit selling 30 hotdogs than 41?Math answer is different from economics answer... opportunity costs, production costs, break even points, multiple other factors. Math answer has nothing to do with reality since the equation is not a true profit calculation. |
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Correct answer is 30 hotdogs... I got it wrong How can he make more profit selling 30 hotdogs than 41?Math answer is different from economics answer... opportunity costs, production costs, break even points, multiple other factors. Math answer has nothing to do with reality since the equation is not a true profit calculation. Which is why it's a rather stupid math question IMHO Seriously, was it that hard for the textbook to ask a relevant question? /parabolas were cool. |
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Quoted: Correct answer is 30 hotdogs... I got it wrong How can he make more profit selling 30 hotdogs than 41?The point, which is very poorly presented in that question, is that the more expensive the hot dogs, the less he sells, and the less expensive the hot dogs, the more he sells. There is, therefore, a point at which the seller maximizes his profits since he sells a goodly number of hot dogs for a goodly sum; selling more hot dogs for less each or fewer hot dogs for more each would result in less profit. So if he sells 30 hot dogs for $3 each, he makes more than if he sold 41 hot dogs for $2 each, for example. All of that background of figuring out how the price impacts the number of hot dogs sold is ignored in the question, which is why it is confusing. |
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Correct answer is 30 hotdogs... I got it wrong How can he make more profit selling 30 hotdogs than 41?Say hot dogs come in packs of 30. If John the Dogger sells 30, there is no waste. If he sells 41 by closing time, he has to open two packs and must throw 19 in the trash. A model like that takes business / regulation rules into effect that say you can't store the 19 hot dogs overnight. Of course, this model implies that selling 60 in a single day is impossible, so it might not be an accurate model. If'n my maths don't escape me... P(x) = -x² + 60x + 71 P'(x) = -2x + 60 2x = 60 x = 30 |
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Quoted: Correct answer is 30 hotdogs... I got it wrong How can he make more profit selling 30 hotdogs than 41?Profit is a curve which curves down, meaning the vertex is a maximum. Calculus? Derivative maximum. The coefficient of the square is a negative one. We should not do your homework. The future depends on you understanding this branch of mathematics. Unless you aspire to be just the server of hot dogs and not a stand owner. Now, why would more product being served result in lower profit? Because you have fixed production means. |
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Quoted: Quoted: Correct answer is 30 hotdogs... I got it wrong How can he make more profit selling 30 hotdogs than 41?Profit is a curve which curves down, meaning the vertex is a maximum. Calculus? Derivative maximum. The coefficient of the square is a negative one. We should not do your homework. The future depends on you understanding this branch of mathematics. Unless you aspire to be just the server of hot dogs and not a stand owner. Now, why would more product being served result in lower profit? Because you have fixed production means. Yep. If a pack of hot dogs and hot dog buns come 6 in a package, then selling 30 would result in maximum profit IF you are given multiple options that aren't multiples of 6. The math makes sense. If I have no way of storing hot dogs and hot dog buns, I'd make less money selling 31 hot dogs than 30 as I would be losing 5 hot dogs and hot dog buns because shit done got sour. |
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Correct answer is 30 hotdogs... I got it wrong How can he make more profit selling 30 hotdogs than 41?The point, which is very poorly presented in that question, is that the more expensive the hot dogs, the less he sells, and the less expensive the hot dogs, the more he sells. There is, therefore, a point at which the seller maximizes his profits since he sells a goodly number of hot dogs for a goodly sum; selling more hot dogs for less each or fewer hot dogs for more each would result in less profit. So if he sells 30 hot dogs for $3 each, he makes more than if he sold 41 hot dogs for $2 each, for example. All of that background of figuring out how the price impacts the number of hot dogs sold is ignored in the question, which is why it is confusing. +1 Generally, the way to sell more hot dogs is to cut the price. The lower the price, the less profit on each, but the more you sell -- depending on the demand for hotdogs at whatever given price. There will be some price/quantity combination that maximizes profit. The math problem boiled this down for you by giving a simple formula for profit as a function of quantity sold. |
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Quoted: John owns a hotdog stand. He has found that his profit is represented by the equation P(x) = -x² + 60x + 71 with P being profits and x the number of hotdogs sold. How many hotdogs must he sell to earn the most profit? 20 hotdogs 31 hotdogs 41 hotdogs 30 hotdogs You could always brute force the bitch. Looking for the max... P(20) = -400 + 1200 + 71, 871 P(31) = - 961 + 1860 + 71, 970 P(41) = -1681 + 2460 + 71, 850 P(30) = -900 + 1800 + 71, 971. Now, derivative of P(x) = -X2 + 60X + 71 is simply -2X+60. Set that to zero so 2X = 60, simple algebra is X = 30. |
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John owns a hotdog stand. He has found that his profit is represented by the equation P(x) = -x² + 60x + 71 with P being profits and x the number of hotdogs sold. How many hotdogs must he sell to earn the most profit? 20 hotdogs 31 hotdogs 41 hotdogs 30 hotdogs You could always brute force the bitch. Looking for the max... P(20) = -400 + 1200 + 71, 871 P(31) = - 961 + 1860 + 71, 970 P(41) = -1681 + 2460 + 71, 850 P(30) = -900 + 1800 + 71, 971. Now, derivative of P(x) = -X2 + 60X + 71 is simply -2X+60. Set that to zero so 2X = 60, simple algebra is X = 30. Holy shit I beat Keith 
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Quoted: Quoted: Quoted: John owns a hotdog stand. He has found that his profit is represented by the equation P(x) = -x² + 60x + 71 with P being profits and x the number of hotdogs sold. How many hotdogs must he sell to earn the most profit? 20 hotdogs 31 hotdogs 41 hotdogs 30 hotdogs You could always brute force the bitch. Looking for the max... P(20) = -400 + 1200 + 71, 871 P(31) = - 961 + 1860 + 71, 970 P(41) = -1681 + 2460 + 71, 850 P(30) = -900 + 1800 + 71, 971. Now, derivative of P(x) = -X2 + 60X + 71 is simply -2X+60. Set that to zero so 2X = 60, simple algebra is X = 30. Holy shit I beat Keith Slow down, you are stroking too fast |
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30 It's a parabola with a minus sign. First derivative = 0 is a maximum. When you post a problem, it should be hard. You suck as a teacher. Get in line behind Phurba. I'm getting lucky tonight 
You already got short stroked. What more do you want? |
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Quoted: If marginal costs increase with each additional unit of production while marginal revenue does not or at a pace greater than marginal revenue there will be a point where anything past that point will actually bring in less profit. Quoted: Quoted: Correct answer is 30 hotdogs... I got it wrong How can he make more profit selling 30 hotdogs than 41?Math answer is different from economics answer... opportunity costs, production costs, break even points, multiple other factors. Math answer has nothing to do with reality since the equation is not a true profit calculation. Which is why it's a rather stupid math question IMHO Seriously, was it that hard for the textbook to ask a relevant question? /parabolas were cool. |
Simple he sells zero hotdogs but goes into massive debt buying all other hotdog manufacturers then with looming bankrupcy he complains to congress that he is too big to fail and that Oscar Myer which he now owns is a american icon and it can't be allowed to go under gets a massive bail out sells the company and retires like a G. 
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Quoted: Correct answer is 30 hotdogs... I got it wrong How can he make more profit selling 30 hotdogs than 41?If he sells more than 30 he has to hire extra help, then he'll have to pay taxes, Obamacare, etc for that new employee. So best to keep it a one man show |