Question

Can someone please help me answer f-I. Please see notes. Thanks

Answer 1

Answer the following questions. Use Equation Editor to write mathematical expressions and equations. First, save this file to your hard drive by selecting Save As from the File menu. Click the white space below each question to maintain proper formatting.

1. Suppose you are an event coordinator for a large performance theater. One of the hottest new Broadway musicals has started to tour and your city is the first stop on the tour. You need to supply information about projected ticket sales to the box office manager. The box office manager uses this information to anticipate staffing needs until the tickets sell out. You provide the manager with a quadratic equation that models the expected number of ticket sales for each day x. ( is the day tickets go on sale).


a. Does the graph of this equation open up or down? How did you determine this?
A: It opens down since the coefficient of x^2 is negative.
b. Describe what happens to the tickets sales as time passes.
A: The number of ticket sales goes down to zero, as x gets larger.
c. Use the quadratic equation to determine the last day that tickets will be sold.
A: x = [-12 +- sqrt(144-4*-0.2*11)]/(-0.4)
x = [-12 +- sqrt(152.8)]/(-0.4)
x = [-12-12.36]/-0.4
x = 60.9 days
On the 61st day, the ticket sales go to zero
Note. Write your answer in terms of the number of days after ticket sales begin.

d. Will tickets peak or be at a low during the middle of the sale? How do you know?
A: The tickets sales during the middle of the sale look at the vertex of the parabola. Since it opens down, we know we have a maximum. This means the tickets sales peak.
e. After how many days will the peak or low occur?
A: This can be determined by finding the x coordinate of the vertex, for this use (-b)/(2a), After plugging in the numbers we get 30, so on the 30th day the peak will occur.
f. How many tickets will be sold on the day when the peak or low occurs?

g. What is the point of the vertex? How does this number relate to your answers in parts e. and f?

h. How many solutions are there to the equation ? How do you know?

i. What do the solutions represent? Is there a solution that does not make sense? If so, in what ways does the solution not make sense?

Answer 2

peak occurs at the vertex. vertex is
\[-\frac{b}{2a}\]

Answer 3

unfortunately you neglected to put in the equation, but i have seen something identical to this, and i believe it was day 30. replace x by 30 and that will give you the ticket sales

Answer 4

was it
\[T=-.2x^2+12x+11\]?

Answer 5

oh you have it already answered in part e. the vertex is (30,191)

Answer 6

f) the peak day is 30 and you will sell 191 tickets
g) this is the same as the vertex which is (30,191)
h) there are two solutions to the quadratic equation, but only one makes sense because one is negative and you cannot go backwards in time

Answer 7

i guess that was h and i together in one sentence

Answer 8

Thank you so much to all that have helped on this one.