A meat department manager discovers that she can sell m(x) kilograms of ground beef in a week, where m(x) = 14700 - 3040x, if she sells it at x dollars per kilogram. She pays her supplier $3.21/kg for the beef.
a) Determine an algebraic expression for p(x), where p(x) represents the total profit in dollars for 1 week.
b) Find the equation for the inverse relation. Interpret its meaning.
c) Write an equation in function notation to represent the price that will earn $1900 in profit. Evaluate and explain.
d) Determine the price that will maximize profit.
e) The supply cost drops to $3.10/kg. What price should the manager set? How much profit will be earned at this price?