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Anj Estrada

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/files/483341/Technical_Worksheet_for_project1.docx

If the links doesn't work, here is a copy.

Project on Math 134 Business Calculus, Summer 2015-2016

Project Due: 07 June 2016

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 6 members, each bringing their own individual strengths to the group. You will submit your work, neatly hand-written and clearly labelled. 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 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 donation 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.

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. Provide a sketch of graph.

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. Provide a sketch of graph.

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.)

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)?

Here is the technical worksheet:

Technical Worksheet

Group __________________

1. The linear price-demand function is p = D(x) = __________________________

Domain: _________________________________

2. The revenue function is R(x) = ______________________________

Domain: _________________________________

3. The cost functions for each of the two possible catering services in terms of x are

CA (x) = _______________________________________ and

CB (x) = _______________________________________.

CB (x) = _______________________________________.

4. Catering Service A will at least break even at a minimum of ________ banquet attendees and a maximum of _______ banquet attendees.

Catering Service B will at least break even at a minimum of ________ banquet attendees and a maximum of _______ banquet attendees.

5. The profit functions for each of the possible Contractors in terms of x are

PA (x) = ____________________________________________ and

PB (x) = ____________________________________________.

PB (x) = ____________________________________________.

6. 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 banquet’s profit since the profit using Catering Service A is \$_____________ and the profit using Catering Service B is \$____________.

7. If the projected sales are 200 banquet tickets at a unit price of \$__________, your company should choose Catering Service ______ in order to maximize the banquet’s profit since the profit using Catering Service A is \$____________ and the profit using Catering Service B is \$____________.

8. The average cost function for Catering Service A is CA(x)=_______________________________.

a. The average cost per attendee if 50 tickets are purchased is CA(50) \$______________.

b. The average cost per attendee if 400 tickets are purchased is CA(400) \$______________.

b. The average cost per attendee if 400 tickets are purchased is CA(400) \$______________.

9. On average, the expected value of spontaneous donations is \$_____________ per attendee.

10. The Committee would like to recommend Catering Service _________.

Number of Attendees for Maximum Profit: ______________

Maximum Charity Ticket Profit: \$______________

Optimal Number of Attendees: ______________

Optimal Charity Ticket Profit: \$______________

Banquet Ticket Price for Maximum Profit: \$______________

Optimal Banquet Ticket Price: \$______________

Maximum Expected Spontaneous Donations: \$______________

Optimal Spontaneous Donations: \$______________

Hope the problem is clear and I hope you can help me! Thank you very much :)