College Algebra Project: Investigate
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Introduction
The goal of this activity is to find the price at which an
airline might receive the most revenue from the
number of nsuper Snacks" sold on some of their flights.
Air PostCorona decided to start charging for snacks on
flights that last longer than 90 minutes. All their planes
are 132-passenge r jets.
2.50
2.50
3
3
3.50
3.50
4
4
4
4.50
4.50
4.50
5
5
5
5
5.50
5.50
5.50
6
6
6
6.50
7
The airline put together a Super Snack that consisted of
a sandwich, mixed fruit, potato chips, and a giant
cookie. They decided it was a service to provide snacks
to the passengers but wanted to maximize their
revenue from the sales as well The Super Snacks cost
them $2 each from an outside vendor. Therefore, they
decided to experiment with the cost of the Super Snack
to see how many would be purchased by passengers at
different prices. To keep the data comparable, they
began offering the snacks on flights that began between
11:00 am. and 1:00 p.m. and that lasted over 90
minutes.
23
24
18
21
20
18
15
14
15
13
11
15
13
15
16
12
9
8
10
8
9
7
3
1
Table 1
Directions
1. Represent the data in Table 1 with a scatter plot
using price p as the independent variable and
number sold n as the dependent variable.
Be sure to label your axes appropriately.
Scatterplot:
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College Algebra Project: Investigat e
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2. A. Describe the relationship between the number
of Super Snacks sold and the price of the Super
Snack in a sentence or two.
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B. Use the regression capabilities of your
graphing calculator to find an appropriate
algebraic model (best-fit) to represent the
relationship between price p and number
soldn.
3. The airline decides to investigate the situation
further. The Air PostCorona is interested in the
revenue (in dollars $) from the sale of Super
Snacks at each of the different prices.
A
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How do you compute the revenue?
B. Compute the revenue for each price shown
and complete the table.
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2.50
3
3
3.50
3.50
4
4
4
4.50
4.50
4.50
5
5
5
5
s.so
s.so
s.so
6
6
6
6.50
7
24
18
21
20
18
15
14
15
13
11
15
13
15
16
12
9
8
10
8
9
7
3
1
2
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College Algebra Project: Investigate
Place vour work/solution s in the column at the riaht.
4. Use your graphing calculator to construct a
scatter plot of price vs. revenue where price is the
independe nt variable. (You don't need to show
this scatterplot on paper.)
A Describe the pattern in the data.
B. Why do you expect to find a maximum
revenue?
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5. Use the regression capabilities of your graphing
calculator to examine different algebraic models
Oinear, quadratic, and cubic) for using price to
predict revenue.
Graph each equation Oinear, quadratic, and
cubic), one at a time, on your scatterplot to
determine which one appears to be the best fit for
the data.
A Give the formula for the model that best
fits the data.
B. Naturally, the airline will want to charge a
price that produces the most revenue. Use
your graphing calculator to determine the
price at which the maximupt revenue will
occur.
6. A What price do you believe the airline should
charge?
B. Why might a price of $4 or $5 be more
practical than a price of$4.50?
3