You manage a movie theater that can handle up to $8,000$ patrons per week. The current demand, price, elasticity for ticket sales, and popcorn information are given in below. The theater would like to keep $45\%$ and above revenues from ticket. Due to the fact that popcorn is on sale and assume each patron will buy a can of popcorn when they buy tickets. Assuming linear demand curves, how can the theater maximize profits?