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. 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. 4. Determine the break-even quantities for each of the two possible catering services. 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.
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.
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.
4. Determine the break-even quantities for each of the two possible catering services.
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. Find the Profit function, P(x)P(x) , for each of the two possible catering services in terms of the number of banquet attendees xx .
The profit functions for each of the possible Contractors in terms of xx are
PB(x)=PB(x)= ____________________________________________.
6. If it is projected that there will be 100 tickets sold at a dinner price of $115.50, which catering service should the committee recommend in order to earn the most profit for the charity?
If the projected sales are 100 banquet tickets at a unit price of $115.50, 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. Decide which catering service your company should choose if the projections yield 200 attendees. Include the ticket price at this demand.
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 $____________.
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