A company sells 30 units of its product each week and can sell an additional 4 units for every $2.50 decrease in its regular price. If the initial price per unit is $50.00, find...

(a) The price p(x) at the production level x, as a function of x. (Hint: Start by letting r be the number of $2.50 decreases in price, then express x as an expression involving r and solve this equation for r. Next, write down an expression for the price, first in terms of r. Substitute the expression you found for r into your price equation to find p(x) in terms of the variable x.)

(b) The revenue R(x) generated from the sale of x units, each at price p(x) (Hint: Writethis as a function of the production level x)

(c) Find the production level x at which revenue is maximized. Determine this maximum revenue. How many decreases in price should be applied from the initial price to reach the maximum revenue?