Overview:The Company you are working for has decided to put on a banquet to raise money for a charity and must decide between two catering services to supply the food and servers. You have been assigned to the Banquet Planning Committee. You should work in a group with up to 4 members, each bringing their own individual strengths to the group. You will submit your work, neatly hand-written and clearly labeled. You must use algebra to solve the problems (not graphing calculator features). To best maintain accuracy, round only your final answers. Simplify completely.
Research Provided: The Company's research department has provided the following estimates: . A demand of 275 banquet attendees can be expected at a dinner plate price of $78.00 each. A demand of 380 banquet attendees can be expected at a dinner plate price of $39.00 each. - Catering Service A has a xed cost of $2,000 and a marginal cost of $27 for each plate. . Catering Service B has a xed cost of $3,100 and a marginal cost of $19 for each plate. . Costs for both caterers include the food, drinks, plates, utensils, tablecloths, glasses, crew, and cleanup. . Dinner plates will only be sold as an entire unit. To justify company resources and to ensure the event will benet the charity, the CEO insists the tickets be sold for no less than $25. All prots will go toward a charity of the committee's choosing. . Additional spontaneous donation to the charity will be accepted the night of the banquet. Studies estimate that 7% will give $5, 21% will give $20, 16% will give $31, 2% will give $100, and 1% will give $420. Analysis: Your group should perform the following analyses: 1. Assume the price-demand function is linear. Use the research estimates to nd the relationship between the price p, and the number of banquet attendees demanded, x. Find the relevant domain. 2. Find the revenue function, R(x), in terms of the number of banquet attendees x. Find the relevant domain by considering realistic limitations on the number of attendees and on price. Provide a sketch of graph. 3. Assume the cost function is linear and use the research estimates to nd the cost function for each of the two possible catering services in terms of the number of banquet attendees x. Provide a sketch of graph. 4. Determine the break-even quantities for each of the two possible catering services. 5. Find the Prot mction, P(x), for each of the two possible catering services in terms of the number of banquet attendees x. 6. If it is projected that there will be 100 tickets sold at a dinner price of $120, which catering service should the committee recommend in order to earn the most prot for the charity? 7. Decide which catering service your company should choose if the projections yield 270 attendees. Include the ticket price at this demand. 8. 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 420 tickets are purchased. 9. On average, how much can you expect to receive in spontaneous donations for each banquet attendee? (Determine the per person expected value (weighted average) of donations.)
