Question

Based off previous events, a demand of 260 banquet attendees is expected at a dinner plate price of $55.00 each. A demand of 340 banquet attendees is expected at a dinner plate price of $35.00 each.
 Your facility can hold up to 500 attendees. There is no rental fee for use of the facility.
 You have two catering companies to choose from:
o Catering Service 1 has a fixed cost of $2,250 and a variable cost of $20 per plate.
o Catering Service 2 has a fixed cost of $2,800 and a variable cost of $14 per plate.
o Costs for both caterers include the food, drinks, plates, utensils, tablecloths, glasses, crew, and cleanup. (That is, there are no other costs to consider.)
 Dinner plates will only be sold as an entire unit (i.e., you can’t sell half of a plate).

A. The price-demand function in terms of x is.
?=?(?)= __________________________________________ Domain: ______ ≤ ? ≤ _________.
B. The revenue function in terms of x is
?(?)= _______________________________________________ Domain: ______ ≤ ? ≤ _________.
C. The cost functions for each of the two possible catering services in terms of ? are
?1(?)= _____________________________________________
?2(?)= ______________________________________________
D. The profit functions for each of the possible catering services in terms of x are
?1(?)= _____________________________________________
?2(?)= _____________________________________________
E. Catering service 1 will break even at a minimum of ___________ banquet attendees.
Catering service 2 will break even at a minimum of ___________ banquet attendees.
F. If the projected sales are 275 banquet tickets,
a. The price per ticket is $__________________.
b. The profit using catering service 1 is $__________________.
c. The profit using catering service 2 is $____________________.
d. Your company should choose catering service # ______ to maximize the banquet’s profit.

Answer 1

The price - demand function, Revenue function, Cost functions for each catering service, Profit functions for each catering service and break even points are as follows: