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 will submit your work, neatly hand-written or typed and clearly labelled. You will submit graphs separately via the Desmos share tool. You must use algebra to solve the problems and describe how to use Desmos or a graphing calculator to check you work. 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 330 banquet attendees can be expected at a dinner plate price of $70.00 each. A demand of 470 banquet attendees can be expected at a dinner plate price of $40.00 each. Catering Service A has a fixed cost of $1,800 and a marginal cost of $30 for each plate. Catering Service B has a fixed cost of $2,500 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. 8. Find the average cost function for Catering Service A. Evaluate the average cost per attendee if 40 tickets are purchased. Evaluate the average cost per attendee if 500 tickets are purchased. The average cost function for Catering Service A is C¯A(x)=C¯A(x)= _______________________________. a. The average cost per attendee if 40 tickets are purchased is CA(40)CA(40) $______________. b. The average cost per attendee if 500 tickets are purchased is CA(500)CA(500) $______________. 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.) On average, the expected value of spontaneous donations is $_____________ per attendee. 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)? 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: $______________
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 will submit your work, neatly hand-written or typed and clearly labelled. You will submit graphs separately via the Desmos share tool. You must use algebra to solve the problems and describe how to use Desmos or a graphing calculator to check you work. 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 330 banquet attendees can be expected at a dinner plate price of $70.00 each. A demand of 470 banquet attendees can be expected at a dinner plate price of $40.00 each.
- Catering Service A has a fixed cost of $1,800 and a marginal cost of $30 for each plate.
- Catering Service B has a fixed cost of $2,500 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.
8. Find the average cost function for Catering Service A. Evaluate the average cost per attendee if 40 tickets are purchased. Evaluate the average cost per attendee if 500 tickets are purchased.
The average cost function for Catering Service A is
C¯A(x)=C¯A(x)= _______________________________.
a. The average cost per attendee if 40 tickets are purchased is CA(40)CA(40) $______________.
b. The average cost per attendee if 500 tickets are purchased is CA(500)CA(500) $______________.
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.)
On average, the expected value of spontaneous donations is $_____________ per attendee.
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)?
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: $______________
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