Show and explain your work. Draw box(es) around your final answer(s). Use algebraic methods unless otherwise stated.

A clothing store sells men's hats for $30 each. At this price, the store sells 100 men's hats per week. The owner estimates that for every $1 increase in price, one fewer men's hat is sold per week.

a) Write a function to model this situation. Use the function to determine the price per hat which would make the greatest revenue per week.

b) Determine the number of hats that would be sold if the owner decided to sell the hats for $75 each.