Maths question please help

The regular airfare between Sydney and Melbourne is $500. An airline using planes with a capacity of 300 passengers on this route observes that they sell an average of 180 tickets. Market research tells the airlines' managers that each $5 fare reduction attracts 3 more ticket purchases per ight. Let N be the number of tickets sold F be the fare R = NF be the total revenue. In this problem the goal is to determine the fare F that will maximise the total revenue. a. Write down an expression for the number of tickets sold for a given fare. As noted in the question, the usual number of tickets sold when the fare is $500 is 180 and ticket salas increase by 3 for each $5 reduction. (2 marks) The maximum fare that will be considered is $500. Given the capacity of the plane, calculate the minimum fare that should be considered. (1 mark) Write down an expression for the total revenue R in terms of F only. (I mark) Sketch R as a function of F over the range of allowable farm. You may draw this neatly by hand, or use Maple or other software. (1 mark) Find the maximum total revenue, the fare which gives the maximum, and the number of tickets sold. You must give sufcient working to demonstrate that you have found the global maximum, which means you must check endpoints, critical points if any, and use the second derivative test