. Currently, an artist can sell 280 paintings every year at the price of $90.00 per painting. Each time he raises the price per painting by $10.00, he sells 5 fewer paintings every year. Assume the artist will raise the price per painting a times. The current price per painting is $90.00. After raising the price x times, each time by $10.00, the new price per painting will become 90+10x dollars. Currently he sells 280 paintings per year. It's given that he will sell 5 fewer paintings each time he raises the price. After raising the price per painting x times, he will sell 280-5x paintings every year. The artist's income can be calculated by multiplying the number of paintings sold with price per painting. If he raises the price per painting a times, his new yearly income can be modeled by the function: f(x)=(90+10x)(280 - 5x) where f(x) stands for his yearly income in dollars. Answer the following: (a) How many paintings the artist must sell in order to obtain the maximum profit? What is the maximum profit? (b) To earn $37, 500.00 per year, the artist could sell his paintings at two different prices. Find those prices.