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?
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
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).
What is the exact equation?
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 x-coordinate of the vertex. Can you determine the vertex of this parabola?