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