In the summer of 2013, Nintendo dropped the price of the Wii U game system in response to a sales slump. It worked: in the following month, they sold three times as many consoles in North America. But did Nintendo end up leaving money on the table?

Students use linear equations to model demand and per-unit profit for the Wii U. They then use that information to develop a quadratic equation that relates retail price and total profit in order to find the price that would have led to the highest possible profit for Nintendo.

Students will

Use historical data to determine the amount of monthly revenue generated by the Wii U at different prices

Model the profit Nintendo earns for each sale of a Wii U console using a linear equation

Construct a linear equation that models demand for a game console in terms of its retail price, and interpret its important features in the context of game console sales

Combine two linear relationships in order to produce and graph a quadratic equation that describes the relationship between retail price and total profit

Use symmetry arguments to find the maximum value of a parabola and interpret its coordinates as the profit-maximizing price and total profit

Discuss the other factors, besides price, that Nintendo might have taken into account in order to make its decision about the Wii U discount

Before you begin

Students should be able to write the equation of a line given two points, and they should be able to interpret the important features of a linear equation. Some familiarity with quadratic function will also be useful, though this lesson can be used to teach students how to find the maximum of a quadratic function given its roots.

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Building Functions (BF), Interpreting Functions (IF), Linear, Quadratic, and Exponential Models (LE)

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Mathalicious lessons provide teachers with an opportunity to teach standards-based math through real-world topics that students care about.

How have video game console speeds changed over time? Students write an exponential function based on the Atari 2600 and Moore's Law, and see whether the model was correct for subsequent video game consoles.

Topic:
Building Functions (BF), Interpreting Categorical and Quantitative Data (ID), Interpreting Functions (IF), Linear, Quadratic, and Exponential Models (LE)