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Activity 2: T-shirt Simulation
(One class period)
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Explain to students that they will design a T-shirt or a pair of sneakers and collect data on how
much other students would be willing to pay for the shirt or sneaker.
Once it has been designed, allow students five minutes to survey their classmates regarding how
much they would be willing to pay for various designs. On the organizer, students should make tick
marks by each price indicating the number of students who would pay that price. For instance, if a
student says that she would pay up to $12 for the shirt, a tick mark should be made on the line
next to $12. If a student says that he would not buy the shirt at all, a tick mark should be made
next to $0.
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Students should then plot the data on a graph of Cost in Dollars versus Number Sold. However, it is
important that students take into account that if a classmate states that they would buy the shirt
for a particular price, it can be assumed that they would also buy the shirt for any price less
than that. For instance, if a student says she would pay $12 for the shirt, it can be assumed that
she would buy the shirt for $1, $3, $8, or any price up to $12. This should be reflected in the
graph. As a result, the graph will represent a negative correlation; a possible graph is shown below.
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When students have plotted the data, they should estimate a line of best fit; that is, they should
draw a line that roughly approximates the data. As an example, a possible line of best fit is shown
in the graph above.
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Based on their graphs, students should answer the following questions:
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How many shirts would you sell if you gave them away for free; that is, how many would
you "sell" at a price of $0?
(Answers will vary, depending on the students' data. Using the graph above, the straight
line implies that approximately 40 shirts would be sold at $0. However, students should
realize that the number is likely much higher-people who wouldn't be willing to pay even
$1 for the shirt might be willing to take it for free. Consequently, the line is useful for
modeling the situation, but it may not be completely accurate for all situations.)
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At what price will you sell no shirts? That is, what price is higher than anyone would be
willing to pay?
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(Answers will vary, depending on the students' data. Using the graph above, it appears
that $18 is more than anyone would be willing to pay. Students should recognize that the x
intercept represents the point at which the price is too high.)
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For what price would you bring in the most total revenue?
(Answers will vary. Using the graph above, it seems that the maximum revenue will occur
when the price is $9; at this price, approximately 20 shirts will be sold, resulting in total
revenue of 9 × 20 = $180. By comparison, 22 shirts will be sold at $8, yielding a revenue
of 8 × 22 = $176; likewise, 17 shirts will be sold at $10, yielding $170. As the price
decreases, more shirts are sold, but less money is earned per shirt; for example, 35 shirts
would be sold at $2, but this only yields $70 total. As the price increases, more money is
earned per shirt, but fewer are sold; for example, at $16, only 4 shirts are sold, yielding
just $64 in revenue.)
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The third question above is challenging to answer, and students should be allowed a few minutes to
struggle with the question in their groups. You may wish to lead a brief discussion about how the
total revenue could be calculated, and you should help the students to realize that revenue is equal
to the product of the number of shirts sold and the price at which they are sold. For instance, using
the graph above, if the shirts were sold at $10, it appears that 19 shirts would be sold;
consequently, the total revenue is $10 × 19 = $190.
Because the calculations to determine maximum total revenue are long and tedious, explain to
students that there is an easier way to find this value. Remind students that the total revenue is
found by multiplying the number of shirts sold by the price at which they were sold. The number of
shirts is given by the line of best fit, and students should write an equation that models the line of
best fit. For example, the line of best fit in the example above passes through the points (0,40) and
(18,0), so the slope of the line is
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The y intercept of the line is 40. Therefore, a fairly accurate equation of the line of best fit is n =
2.2p + 40, where n is the number of shirts sold, and p is the selling price.
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Have students determine the slope, y intercept, and an equation for their line of best fit.
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Then, explain that since p represents the selling price of the shirts, the total revenue can be found
by multiplying the number sold by p. This multiplication will result in a quadratic equation. For
instance, using the fictitious example above, the total revenue r is given by the equation
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Using a spreadsheet program, a graphing calculator, or paper and pencil, students should graph
this quadratic equation. The vertex of the equation represents the selling price at which the
maximum total revenue would be earned. For the example above, the maximum revenue is about
$180 which occurs when the selling price is around $9.
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Based on their graphs, students should determine the selling price at which revenue will be
maximized.
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To conclude this portion of the lesson, tie together all of the elements: that the demand for the
shirts, as indicated by the amount that classmates would be willing to pay for them, dictates the
price that should be charged. It also affects the number of shirts that should be produced; produce
more shirts than will sell, and money is wasted on production and materials.
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Supply and Demand Questions
1. A new video game system is released just before Christmas, and everyone's
"gotta have it." As parents race to the store to buy the system for their kids, the
price throughout December holds steady at $349.99. What do you think will
happen to the price in January? …February? …June?
2. Local stores sell a fleece jacket for about $50. Sales of the jacket are good,
but not great. However, when consumers learn that Lebron James wears this
jacket, sales increase. What do you think will happen to the price? (Note to
teacher: You may wish to replace the reference to Lebron James with a sports
hero in your area.)
3. When a motorcycle manufacturer announces that it will no longer make its
most popular model of bike, what do you think will happen to the price of the
bike?
4. Mrs. Taylor sells chocolate molasses cookies. They are delicious, and she is
the only one in town who makes them. However, when Ms. Brown moves to
town, she begins to make cookies, without any difference in quality or beauty
from Mrs. Taylor's cookies. What will likely happen to the price of Mrs. Taylor's
cookies?
Answers to Questions:
1. Demand will likely decrease; that is, people who have bought the system
don't need to buy it again, so fewer potential customers will remain.
Consequently, the price should decrease.
2. Demand increased, so the price will likely go up. (Note to teacher: You may
wish to replace the reference to Lebron James with a sports hero in your area.)
3. Demand has not changed, but the supply has decreased, so the price will
probably go up.
4. Price should go down, because supply increased.