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. 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 r. Provide the graph using Desmos. The cost functions for each of the two possible catering services in terms of r are CA(x) = CB(x) = and 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.