An Albertabased NHL team is struggling to fill its seats. When the average ticket price is $250, the team sells an average of 8000 tickets. However, when the average price is reduced to $150, the team sells an average of 16000 tickets. The relation of sold tickets (1(33) as a function of their average price :13 is assumed to be linear. Find the function 9(13). What should the average ticket price be in order to maximize revenue? Round your answer to two decimal places. (Hint: Use the revenue function ROB) : mq(m)) Check An apartment complex has 100 units. The monthly profit (in dollars) from renting out :13 apartments is given by the function Ixm)=Jm2+15mmMmm) How many units should be rented out to maximize monthly profit? Answer: Q What is the maximum monthly profit? Answer: $ E Check (184m) 2:13 in exact form [no approximations). Enter DNE if there are no critical points. Answer: Critical point(s} = E Find the critical point[s) of the function at) : , if any, leaving your answer(s} Check The cost of manufacturing :1? badminton rackets per day is given by the function C(32) : 650 + 5:: + 0.000232 Each racket can be sold at a price ofp dollars, where p : 10 0.0003213. Find the number of rackets to be manufactured which maximizes the daily profit for the company Answer: E Check Consider the function f($) : m6 111 :13 (a) Find the domain of f. Answer: (\\:l, E) (b) Find the critical points. (c) Find the domains of increase and decrease. Increasing l: E) l) Decreasing. [l (d) Find the inflection point. Consider the function x) = Em (a) Find the domain of f. Answer: [E E) (b) Find the local maximum. Answer: (:13; 'il) :( . l (c) Find the domains of increase and decrease. Increasing: (\\_/, \\_/) U (\\_/, \\_/) Decreasing: (E,E) (d) Find the inflection points. Check You will have 5 attempts for the first three parts of this problem. You will have 1 attempt for the last part of this problem. For 2 a: , 10:13 (I: : . m2+5' ) (::r:2+5)2 1'01?) = Find the :1? component of the critical point. [Please use exact values which might include square roots or exponentials etc. No decimals} w =: The interval of decrease is (i:l, \\:i]. The interval of increase isd:i, \\:i) The critical point is a {You have one attempt for this part} 0 local minimum 0 local maximum 0 neither Consider a function f such that f'(:1:): (m2 8):?1'. Then: 0 at) has a local minimum at :13 = S an) has a local maximum at :1: : E o an) is concave down over the interval (E! E) Check Let at) be a function defined for all m E R and such that: 0 f'(:12) is differentiable, with only two critical numbers at a\": = 6 and :12 = 9; o f"(113)> Uwhen :3 Z) 0, and f"(:13)