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. 1. Assume the price-demand function is linear. Use the research estimates to find the relationship between the price pp, and the number of banquet attendees demanded, xx . Find the relevant domain. The linear price-demand function is p=D(x)=p=D(x)=  __________________________ Domain: _________________________________ 2. Find the revenue function, R(x)R(x) , in terms of the number of banquet attendees, xx . Find the relevant domain by considering realistic limitations on the number of attendees and on price. Provide the graph using Desmos. The revenue function is R(x)=R(x)=  ______________________________ Domain: _________________________________ 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 xx . Provide the graph using Desmos. The cost functions for each of the two possible catering services in terms of xx are CA(x)=CA(x)=  _______________________________________ and CB(x)=CB(x)=  _______________________________________.​

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.

1. Assume the price-demand function is linear. Use the research estimates to find the relationship between the price pp, and the number of banquet attendees demanded, xx . Find the relevant domain.

The linear price-demand function is p=D(x)=p=D(x)=  __________________________
Domain: _________________________________

2. Find the revenue function, R(x)R(x) , in terms of the number of banquet attendees, xx . Find the relevant domain by considering realistic limitations on the number of attendees and on price.

Provide the graph using Desmos.

The revenue function is R(x)=R(x)=  ______________________________
Domain: _________________________________

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 xx .

Provide the graph using Desmos.

The cost functions for each of the two possible catering services in terms of xx are