18. Ticket Price Optimization Dalmatian Airlines also flies a daily flight from Los Angeles to Sacramento. Currently they sell each ticket for $100, and on average 200 people take the flight, so their revenue per flight is 200 tickets x $100/ticket = $20,000. They are interested in seeing whether they can increase their revenue by changing the price of a ticket. Based on market research they dis- cover that for every $2 increase in ticket price, one fewer person will buy a ticket. Similarly for every $2 decrease in ticket price, one more person will buy a ticket. (a) What ticket price would maximize Dalmatian Airlines' rev- enue? (Hint: Denote the number of extra people flying on the route due to a price change by x, and the cost of a ticket by $1002x. Then explain why the revenue to be maximized is R(x) = (100 2x)(200 + x). You should also explain what the domain of this function is.) (b) The plane can seat a maximum of 250 people. How does this information change the domain of R(x)? Does this constraint af- fect your answer to part (a)? 18. Ticket Price Optimization Dalmatian Airlines also flies a daily flight from Los Angeles to Sacramento. Currently they sell each ticket for $100, and on average 200 people take the flight, so their revenue per flight is 200 tickets x $100/ticket = $20,000. They are interested in seeing whether they can increase their revenue by changing the price of a ticket. Based on market research they dis- cover that for every $2 increase in ticket price, one fewer person will buy a ticket. Similarly for every $2 decrease in ticket price, one more person will buy a ticket. (a) What ticket price would maximize Dalmatian Airlines' rev- enue? (Hint: Denote the number of extra people flying on the route due to a price change by x, and the cost of a ticket by $1002x. Then explain why the revenue to be maximized is R(x) = (100 2x)(200 + x). You should also explain what the domain of this function is.) (b) The plane can seat a maximum of 250 people. How does this information change the domain of R(x)? Does this constraint af- fect your answer to part (a)