Currently, an artist can sell 270 paintings every year at the price of $150.00 per painting. Each time he raises the price per painting by $15.00, he sells 5 fewer paintings every year.
Assume the artist will raise the price per painting z times.
The current price per painting is $150.00. After raising the price z times, each time by $15.00, the new price per painting will become $150 + 15z dollars.
Currently he sells 270 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 z times, he will sell 270 - 5z paintings every year.
Per painting z times, his new yearly income can be modeled by the function:
f = 150 + 15z * (270 - 5z)
where f stands for his yearly income in dollars
Answer the following questions:
1. To obtain maximum income of f, the artist should set the price per painting at $225.
2. To earn $73,125.00 per year, the artist could sell his paintings at two different prices. The lower price is $150 per painting, and the higher price is $225 per painting.
