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 $1,800 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. 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)___________________. a. ) The average cost per attendee if 40 tickets are purchased is ? C a(40) $. b. )The average cost per attendee if 500 tickets are purchased is ??C a(500) $. 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.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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 $1,800 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.

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)_______________________________.

a. ) The average cost per attendee if 40 tickets are purchased is ? C _a(40) $______________.

b. )The average cost per attendee if 500 tickets are purchased is ??C _a(500) $______________.

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.

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