Anonymous asked in Science & MathematicsMathematics · 8 years ago

Ticket sales (math Class). No previous solutions have this equation..?

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). tickets = -0.4x^2+12x+6

a.) Does the graph of this equation open up or down? How did you determine this? (show work)

b.) Describe what happens to the tickets sales as time passes.

c.) Use the quadratic equation to determine the last day that tickets will be sold.

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?

e.) After how many days will the peak or low (middle of the sale) occur?

f.) How many tickets will be sold on the day when the peak or low (middle of the sale) occurs?

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

h.) How many real solutions are there to the equation -0.4x^2+12x+6 = 0? 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?

1 Answer

  • Anonymous
    8 years ago
    Best Answer

    c.) -0.4x² + 12x + 6

    a = -0.4

    b = 12

    c = 6

    x = [-b ± √(b² - 4ac)]/(2a)

    x = [-12 ± √((12)² - 4(-0.4)(6)]/(2(-0.4))

    x = [-12 ± √153.6]/-0.8

    x ≈ -0.49 or 30.49

    Although the negative value satisfies the equation, -0.49 days doesn't make sense for your problem (unless you can travel backwards in time), so we reject it.

    x ≈ 30.49 days

    Which means the last tickets will be sold on the 30th day after ticket sales begin.

    e) Take the first derivative and set it equal to zero:

    f'(x) = 0

    -0.8x + 12 = 0

    0.8x = 12

    x = 12/0.8

    x = 15 days

    f''(x) = -0.8

    since f''(x) is negative, the curve opens down, meaning that the critical point x = 15 is a MAXIMUM.

    f.) Evaluate the ticket sales when x = 15:

    f(15) = -0.4(15)² + 12(15) + 6

    f(15) = -90 + 180 + 6

    f(15) = 96 tickets

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