Music and Money
The rising stars of the band Red Rockers are trying to make enough money to put together a tour of
Utah and Idaho. In order to do so they understand they need to maximize profit for all their remaining
shows for the summer. Their manager estimates the band’s profit p for a concert by using the function
p(t)=-200t2+2500t-c, where t is the price per ticket and c is the band’s operating cost. What is the
maximum value of the graph if the operating cost for a venue is $500?
What does the maximum value represent?
What is the significance of the t-coordinate of the maximum point?
The table shows the band’s operating cost at three different concert locations. What range of ticket
prices should the band charge at each location in order to make a profit of at least $1000 at each
concert?
Band’s Costs
Location
Freemont Park
Saltillo Plaza
Riverside Walk
Which venue looks to be the most profitable? Why?
Operating Cost
$900
$1500
$2500