Optimization by Graphing

You are on a committee to plan for a school dance and need to decide how much to charge for a ticket. Last year you charged $5.00 and sold 400 tickets. Earlier experiences suggest for every 10ยข decrease in price you will sell an extra 50 tickets. Write a function and graph to find the optimum price.

x = change in a value

Profit = (ticket cost)(tickets sold)





max (21, 4205)

x = 21

ticket cost = 5-0.10x

ticket cost = 5-0.10(21)

ticket cost = $2.90