Question

For Questions 13 and 14: A national food service runs food concessions for sporting events throughout the country. The company's marketing research department chose a particular football stadium to test market a new jumbo hot dog. It was found that the demand for the new hot dog is given approximately by p = 8 - 2inx for 5 SX 850 where x is the number of hot dogs (in thousands) than can be sold during one game at a price of Sp. 4 POINTS Question 13) Find the local extrema for the revenue function. 4 POINTS Question 14) On which intervals is the graph of the revenue function concave upward? Concave Downward? 4 POINTS Question 15) Find the point of diminishing return for the function R(x) = (600x2 - x) for 0 < x < 400 where R is the revenue (in thousands of dollars) and x is the advertising cost (in thousands of dollars). serol ir through 19 l'Hnnital's nule lif it anplies to find each limit. If L'Hopital's rule does not

Answer 1

- 8-2lna ssa? So Revenue = dem and x price Rla) = (x). (8-267x) = 82 - 2a ln x 103 ) function local extrema for the revenur R'(a) = 0 + d (82 - 2a ena) = 0 da a - - 8-2[2.44 + ina (1)] =0 8-2 [1+ Anx) = 0 enas 3 local entrema at x= e & R(x= e = 803 - 203 ence) = 8es 23 (3) 2.3

8a-2a lona Rica) = 6 -2 enz "re) = -264- Rial i concave down word for .R(a)co Ria) <.0 t E (5,50 Thesefore, down words in it Rla) is concave region of domain.