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Recall the larger goal is to determine whether or not ACME should keep their "Widget Division" in operation. We need to know if they are making a...
Recall the larger goal is to determine whether or not ACME should keep their "Widget Division" in operation. We need to know if they are making a profit off the widgets.
When they charge $375 for a widget, they make 25 sales. Management estimates that for every $10 decrease in the price, an additional two sales are made. Let D denote the number of sales (demand) and p the price in dollars.
A. The relationship between sales and price linear. How do you know?
B. Because of the linear relationship, we can write D as a function of p. What is the slope (x coefficient) of the resulting linear equation?
D(p) = ___ p + ____
C. What is the slope (given by the p coefficient-first blank)? Hint: You can use the slope formula if you have two data points. You were already told that when ACME charges 375 for a "widget", they make 25 sales. So (375,25) is a data point. To get the second data point, drop the price by 10 dollars. What is the number of sales that corresponds to that new price?
D. What is the intercept (given by the constant term-second blank)? That is, how many "sales" will ACME make if they give the "widgets" away for free?
E. Now you can write the linear function. What is the estimated number of sales if ACME charges $345 per widget?
F. Revenue is the amount of money earned. In general, revenue is the product of demand (D, number of sales) and price per unit (p). What is the estimated revenue if ACME charges $345 per widget?
