Business (Widgets, Inc) forms the linear model of its widget pricing function based on given information: Let x represent number of widgets sold, and p(x) price per widget in dollars. Firm starts by selling x = 350 widgets at the set price of $50 each. After holding the "sale", the firm proposes that a $10 discount on price will yield increase of 30 more widgets sold.
(a) Determine linear pricing function p(x) based on information. p(x) =
(b) Based on fact that firm wishes both sales and price to be positive, find suitable domain of pricing function p(x)? Write your answer using interval notation.
(c) Determine revenue function? (revenue is total sales income)
(d) Find sales price p yields maximum revenue?