Question

12. Cindy wants to make more profit on her cupcake stand so she hired a market analyst. The analyst determined that Cindy had accurately estimated her costs (see problem 11) and that her price- demand function is given by p(x) = 6.8 -0.0017 0 SX 3000 where x is the number of cupcakes produced and sold. a. Find the new revenue function for Cindy's cupcake stand. b. Find the new profit function for Cindy's cupcake stand and determine its domain. c. How many cupcakes does Cindy need to sell now in order to break-even?

C(x)=3(×)+370

Answer 1

(6) E(x) = 3x+370 P = 6.8- 0 oulx u LX 23000 IR = P x OLXs sooo Gespx -0.001x2 Poufit - TR - TC = 6.88-0.0018² - 3x-370 = -0.00182 +3-8x - 3.70 At breakeven Point, Rofit=0 Do 0 = -0.001x2 + 3-8x - 370 Solving quadratic equation to get x=3 700 x = 100 Profit is maximized when MR = mc Ge8-0·002X = 3 3.8 -0.00 2x (1 900 = x (d) P = 6-8-0.001 (1900) @=4.9]