Usually, when you purchase a lot in an auction, you pay not only your winning bid price but also a buyer’s premium. At one auction house, the buyer’s premium is 17.5% of the winning bid price for purchases up to $50,000. For larger purchases, the buyer’s premium is 17.5% of the first $50,000 plus 10% of the purchase price above $50,000.

a. Find the total price a buyer pays (bid price plus buyer’s premium) at this auction house for purchases of $1,000, $25,000, and $100,000.

b. Express the total purchase price of a lot at this auction house as a function of the final (winning) bid price. Sketch the graph of this function.