What is the relationship between the price and demand for the Everlasting Gobstopper based on the data provided by Wonka, Inc.?
The marketing department of Wonka, Inc. has provided data showing that the Everlasting Gobstopper's price and demand are inversely related. When the price of the gobstopper increases, the demand decreases, and vice versa. This relationship can be seen in the data points where at a price of $500, the demand is 1.2 million units, but when the price increases to $600, the demand drops to 0.8 million units. To further analyze this relationship, we can develop the linear formula for price as a function of quantity.
Linear Formula Development
To develop the linear formula for price as a function of quantity, we can use the slope-intercept form of a linear equation, which is y = mx + b. In this case, the price (y) is the dependent variable, and the quantity (x) is the independent variable.
First, we need to calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
m = (0.8 - 1.2) / ($600 - $500)
m = -0.4 / $100
m = -0.004 million
Now, let's find the y-intercept (b). The y-intercept represents the price when the quantity is zero. To find the y-intercept, we can use one of the data points given. Let's use the point (1.2 million, $500).
Using the point-slope formula:
y - y1 = m(x - x1)
y - 500 = -0.004(x - 1.2)
y - 500 = -0.004x + 0.0048
y = -0.004x + 500.0048
Therefore, the linear formula for the price as a function of quantity of the Everlasting Gobstopper is:
Price ($) = -0.004 * Quantity (million units) + 500.0048
This formula shows that for every increase in quantity demanded, the price decreases by $0.004 million. It provides valuable insights for Wonka, Inc. to optimize their pricing strategy and maximize revenue based on market demand.