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A-hockey-team-plays-in-an-arena-that-has-a-seating-capacity-of-15-000-spectators-With-the-ticket-price-seat-at-14-average-attendance-at-recent-games-has-been-9500-A-market-survey-indicates-that-fo




Question Number 135230 by benjo_mathlover last updated on 11/Mar/21
A hockey team plays in an arena that  has a seating capacity of 15,000  spectators. With the ticket price  seat at $14, average attendance  at recent games has been 9500.  A market survey indicates that  for each dollar the ticket price  is lowered ,the average attendance  increases by 1000.  (a) Find a function that models  the revenue in terms of ticket  price  (b) Find the price that maximizes  revenue from ticket sales  (c) What ticket price is so high  that no one attends and so no  is generated
$${A}\:{hockey}\:{team}\:{plays}\:{in}\:{an}\:{arena}\:{that} \\ $$$${has}\:{a}\:{seating}\:{capacity}\:{of}\:\mathrm{15},\mathrm{000} \\ $$$${spectators}.\:{With}\:{the}\:{ticket}\:{price} \\ $$$${seat}\:{at}\:\$\mathrm{14},\:{average}\:{attendance} \\ $$$${at}\:{recent}\:{games}\:{has}\:{been}\:\mathrm{9500}. \\ $$$${A}\:{market}\:{survey}\:{indicates}\:{that} \\ $$$${for}\:{each}\:{dollar}\:{the}\:{ticket}\:{price} \\ $$$${is}\:{lowered}\:,{the}\:{average}\:{attendance} \\ $$$${increases}\:{by}\:\mathrm{1000}. \\ $$$$\left(\boldsymbol{{a}}\right)\:\boldsymbol{{F}}{ind}\:{a}\:{function}\:{that}\:{models} \\ $$$${the}\:{revenue}\:{in}\:{terms}\:{of}\:{ticket} \\ $$$${price} \\ $$$$\left({b}\right)\:{Find}\:{the}\:{price}\:{that}\:{maximizes} \\ $$$${revenue}\:{from}\:{ticket}\:{sales} \\ $$$$\left({c}\right)\:{What}\:{ticket}\:{price}\:{is}\:{so}\:{high} \\ $$$${that}\:{no}\:{one}\:{attends}\:{and}\:{so}\:{no} \\ $$$${is}\:{generated} \\ $$

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