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Problem: Rosalie is organizing a circus performance to raise money for a charity. She is trying to decide how much to charge for tickets. From past experience, she knows that the number of people who will attend is a linear function of the price per ticket. If she charges $5, 1200 people will attend. If she charges $7, 970 people will attend. How much should she charge per ticket to make the most money?
 one year ago
 one year ago
Problem: Rosalie is organizing a circus performance to raise money for a charity. She is trying to decide how much to charge for tickets. From past experience, she knows that the number of people who will attend is a linear function of the price per ticket. If she charges $5, 1200 people will attend. If she charges $7, 970 people will attend. How much should she charge per ticket to make the most money?
 one year ago
 one year ago

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LogicalAppleBest ResponseYou've already chosen the best response.1
If you consider these numbers as points, where x = ticket price and y = people then you have P1 = (4, 1200) and P2 = (7, 970) Determine the equation of a line that passes through these points. You will obtain a linear equation of the form y = mx + b. Notice, though, that Profit itself is a function of x and y. In fact Profit = x * y (it equals the number of people multiplied by the ticket price). So your profit equation would be P(x) = x * y = x * (mx + b) Determine the vertex of this profit equation. This will be the point, x (the ticket price) that results in the maximum profit P(x).
 one year ago

rashley284Best ResponseYou've already chosen the best response.0
What is the exact equation?
 one year ago

LogicalAppleBest ResponseYou've already chosen the best response.1
I meant to say P1 = (5, 1200) ******** Well if the points are (5, 1200) and (7, 970), the slope is (1200  970) / (5  7) = 115 In point slope form we can write y  y1 = m(x  x1) y  970 = 115(x  7) y = 115x + 1775 Our profit is x * y or x * (115x + 1775) Profit = P(x) = 115x^2 + 1775x This is a parabola with a maximum value of P(x) where x is the xcoordinate of the vertex. Can you determine the vertex of this parabola?
 one year ago
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