SOLUTION: Pls help me. Steve owns a hotdog stand. He has found that sales of hot dogs average 45,000 hot dogs a year when the hot dogs sell for $2.50 each. For each 50 cent increase in th

Algebra ->  Algebra  -> Finance -> SOLUTION: Pls help me. Steve owns a hotdog stand. He has found that sales of hot dogs average 45,000 hot dogs a year when the hot dogs sell for $2.50 each. For each 50 cent increase in th      Log On

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Question 143223: Pls help me.
Steve owns a hotdog stand. He has found that sales of hot dogs average 45,000 hot dogs a year when the hot dogs sell for $2.50 each. For each 50 cent increase in the price, the number of hotdogs sold drop by 5000. What price per hot dog should Steve charge to realize the maximum revenue?
Answer by vleith(2825) About Me  (Show Source):
You can put this solution on YOUR website!
Revenue = Quantity*Price
Price = 2.50 + 0.0001(45000-Q) Q <= 45000
R+=+Q+%282.50+%2B+4.5+-+0.0001Q%29
R+=+7Q+-+0.0001Q%5E2
R+=+Q+%287+-+0.0001Q%29+
There are several ways to solve this. If you understand calculus, take the first derivative and solve for the max.
If you want to just use simple algebra, find the two places where the Revenue is 0 and then split the difference.
If you are good with parabolas, find the vertex.
whichever way, you find the most revenue selling 35,000 dogs