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.
(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)?
(c) What is the revenue function? (revenue is total sales income)
(d) What sales price p yields maximum revenue?
*I honestly dont know where to start because my teacher has yet to explain this problem to us, but I need to know it for an upcoming test!
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.
(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)?
(c) What is the revenue function? (revenue is total sales income)
(d) What sales price p yields maximum revenue?
*I honestly dont know where to start because my teacher has yet to explain this problem to us, but I need to know it for an upcoming test!
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