and cost (C) with respect speed of 80 miles per hour would have travelled 80 niles (which is the change in distance covered in the journey in one hour. Similarly, marginal give the approximate change in profit P, revenue R aud cost C' for each additional unit o goods sold are usefal tools in investigating the rates of change of proft (F), reveaie (R) o the munber r of unit of goods sold. Using speed as an examplc, a train moving at a profit P(a], marginal revenue R'(a:) and marginal cost C(r), resjectively Example. Mrs. Rose has a business selling pâté in Tampa for over a year. She wants to study the effecet of pricing in her pâté servings on her business. Use x to deuote the umber of servings she sells each month and p to denote the price of each serving that she sells. She is currently selling :t 120 serviugs at estimates that (based on her current customera) she can sell 100 Rervings if she charges p 88. (a) Find the demand equation. (Assume that demand is linear.) S7 each. She (b) Find her monthly revenue as a function of (c) Her monthly cost is C = 100 + 3z. Find her monthly profit as a function of a. (d) Find the marginal profit Px). (e) Mrs. Rose is currently selling z = 120 servings (at $7 each) a month. Evaluate Pr(x) at x-120. (f) Explain the meaning of the numerical value in (e). (g) In view of the answer in (e), which course of action does Mrs. Rose need to take in order to increase her profit? (h) At which price should Mrs. Rose sell her pâté in order to maxinize profit?