Hello I need some help with these 3 questions. If you could please show me all your work on a separate sheet of paper with the solutions/answers that would be great!

4. A professional basketball team plays in a stadium that holds 23,000 spectators. With ticket prices at $60, the average attendance had been 18,000. When ticket prices were lowered to $55, the average attendance rose to 20,000. Based on this pattern, how should ticket prices be set to maximize ticket revenue? 6. A 5,000 m' rectangular area of a field is to be enclosed by a fence, with a moveable inner fence built across the narrow part of the field, as shown. The perimeter fence costs $10/m and the inner fence costs $4/m. Determine the dimensions of the field to minimize the cost. 5. Higher-order derivatives are derivatives that are taken found after a previous derivative has been taken. For example, we can take the first derivative (y') and the second derivative (y") and the 3rd derivative (y") if we are given the original function (y). Quite often, multiple higher- order derivatives can be found. Higher-order derivatives are used in Science (physics) and mathematics (Differential Equations). A differential equation is an equation that contains functions and some higher-order derivatives. Using a formal proof structure (LHS = RHS), prove the differential equation xy' - 3y + y" + 4 = 2x? given the function y = x - 2x3 + 3x