A business (Widgets, Inc) forms a linear model of its widget pricing function based on the following information:
Let x represent the number of widgets sold, and p(x) the price per widget in dollars. The firm begins by selling x = 200 widgets at a set price of $30 each. After holding a "sale", the firm proposes that a $10 discount on the price will yield an increase of 40 more widgets sold.
(a) Find the linear pricing function p(x) based on this information.
p(x) =
(b) Based on the fact that the firm wants both sales and the price to be positive, what is the appropriate domain of the pricing function p(x)?
domain:
Let x represent the number of widgets sold, and p(x) the price per widget in dollars. The firm begins by selling x = 200 widgets at a set price of $30 each. After holding a "sale", the firm proposes that a $10 discount on the price will yield an increase of 40 more widgets sold.
(a) Find the linear pricing function p(x) based on this information.
p(x) =
(b) Based on the fact that the firm wants both sales and the price to be positive, what is the appropriate domain of the pricing function p(x)?
domain: