Please show all your work for this part of the assignment. There are not graphs required here. Please use derivatives to obtain maximum values: f(x)=0

If it is projected that there will be 100 tickets sold at a dinner price of $112.50, which catering service should the committee recommend earning the most profit for the charity? Decide which catering service your company should choose if the projections yield 200 attendees. Include the ticket price at this demand.

Find the average cost function for Catering Service A. Evaluate the average cost per attendee if 50 tickets are purchased. Evaluate the average cost per attendee if 400 tickets are purchased. Interpret the results in each case. Overall recommendations:

Which catering service does your committee recommend to obtain the most profit for the charity?

How many people should attend the banquet to earn that profit and what profit can be expected from the banquet ticket sales? What price would you recommend for each dinner plate (ticket)?

What will be the expected total amount raised for the charity (including the dinner ticket profits)?

Analysis Results If the projected sales are 100 banquet tickets at a unit price of $112.50, your company should choose Catering Service ______ in order to maximize the banquets profit since the profit using Catering Service A is $_____________ and the profit using Catering Service B is $____________.

If the projected sales are 200 banquet tickets at a unit price of $__________, your company should choose Catering Service ______ in order to maximize the banquets profit since the profit using Catering Service A is $____________ and the profit using Catering Service B is $____________. The average cost function for Catering Service A is C (x)=___________________________. The average cost per attendee if 50 tickets are purchased is (C_A ) (50) $______________. This means ______________________________________________________________ ________________________________________________________________________ The average cost per attendee if 400 tickets are purchased is (C_A ) (400) $______________. This means ______________________________________________________________ ________________________________________________________________________ The Committee would like to recommend Catering Service _________. Optimal Number of Attendees: ______________ Optimal Charity Ticket Profit: $______________ Banquet Ticket Price for Maximum Profit: $______________ Optimal Banquet Ticket Price: $______________