Group K Project 1 Math 1395 Business Calculus, Fall 201 5 Technical W orksheet Due: 23 September 2015 Project Due: 30 September 2015 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 team with up to 4 members, each bringing their own individual strengths to the group. A technical worksheet has been provided to document your final answers. You will submit your work, neatly hand-written and clearly labeled, on a separate page. You must use algebra to solve the problems (not graphing calculator features). To best maintain accuracy, round only your final answers. Simplify completely. Resea rch Provided The company's research department has provided the following estimates. A demand of 230 banquet attendees can be expected at a dinner plate price of $80.00 each. A demand of 370 banquet attendees can be expected at a dinner plate price of $45.00 each. Catering Service A has a fixed cost of $1,900 and a marginal cost of $30 for each plate. Catering Service B has a fixed cost of $3,000 and a marginal cost of $22 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 benefit the charity, the CEO insists the tickets be sold for no less than $40. All profits will go toward a charity of the committee's choosing. Additional spontaneous donations to the charity will be accepted the night of the banquet. Studies estimate that 5% will give $5, 23% will give $20, 18% will give $50, 7% will give $100, and 2% will give $500. Analysis Each team should perform the following analyses: 1. Assume the price-demand function is linear. Use the research estimates to find 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. Sketch a graph on the work page. 3. Assume the cost function is linear and use the research estimates to find the cost function for each of the two possible catering services in terms of the number of banquet attendees x. Sketch a graph on the work page. 4. Determine the break-even quantities for each of the two possible catering services. 5. Find the Profit function, 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 $112.50, which catering service should the committee recommend in order to earn the most profit for the charity? 7. Decide which catering service your company should choose if the projections yield 200 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 400 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.) Which charity does the committee recommend for receipt of banquet donations? 10. Overall recommendations: Which catering service does your committee recommend in order 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 dollar amount is expected from spontaneous donations? What will be the expected total amount raised for the charity (including the dinner ticket profits and spontaneous donations)? Project Report Eighty percent of the grade for this assignment is shared by each team member. The ten analysis items, graphical representations, and the writing components will earn a group grade. The final twenty percent is an individual grade. There are 100 points possible. This assignment is 4% of the course grade. Group Components Title Page: The project title page should include the name of the report (Be creative. Do NOT call it Project 1.), the name of the class and the semester, the instructor's name, the date, and the name of each group member listed alphabetically by last name. The spacing and print should be well proportioned. There are very nice cover page layouts available. A photo may be used to incorporate the chosen charity. (10 points) Writing Component (typed): Include a paragraph describing the charity and why your group has chosen it, as well as, a paragraph with the committee's overall recommendation for the company. You should address the questions posed in analysis item 10. Further analysis may be used to develop a well-supported recommendation. Support all additional calculations on the work page. Be professional! (10 points) Graphs: Use technology such as MS Excel to create graphs displaying the important functions that could be used to help explain your recommendation to your company's board members. Note that to best compare items, multiple functions should be on the same graph. Be sure all necessary titles and labels appear on the graph, as you will not be there to explain the graph to the board members. (10 points) Technical Worksheet (provided in MyMathLab/Document Sharing): Include the graded copy (and a corrected copy if values were incorrect on the initial submission). (45 points) Work Pages: These are to be neatly hand-written, organized and labeled. Showing work is required for full credit on the technical worksheet analysis items. If the instructor cannot find a problem quickly or cannot read it, no points will be given. (5 points) Individual Components Individual Project Analysis (provided in MyMathLab/Document Sharing): Each team member should submit a Project Analysis form to Ms. Spellmann. (10 points) Individual Component Worksheet (provided in 'MyMathLab/Document Sharing): At the last minute, additional catering services have made a bid for this event. Each team member must contact Ms. Spellmann in person to get the proposal for one of these caterers. Team members cannot use the same caterer. You must work alone for this part. If someone asks you for help, politely suggest they ask Ms . Spellmann. (10 points) a. Find the cost function for your caterer in terms of banquet attendees X. b. Determine the .break-even quantities for the catering service. c. Find the profit function for your caterer in terms of banquet attendees x. d. Will this caterer provide a higher profit for the charity? Explain in detail. Group Extra Credit: In order to attract only more serious donors, your committee may want to change the minimum dinner plate fee to $85. Provide a new set of recommendations (similar to #10) with this criterion; and add any final recommendations .for the company. REFER TO CLASS NOTES, THE BOOK, AND GROUP MEMBERS FIRST, THEN ASK YOUR INSTRUCTOR IF YOU STILL HAVE QUESTIONS. An instructor consultation is highly recommended prior to the technical worksheet due date