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rashley284
 3 years 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?
rashley284
 3 years 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?

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LogicalApple
 3 years ago
Best ResponseYou've already chosen the best response.1If 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).

rashley284
 3 years ago
Best ResponseYou've already chosen the best response.0What is the exact equation?

LogicalApple
 3 years ago
Best ResponseYou've already chosen the best response.1I 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?
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