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 Profit function, P(x) , for each of the two possible catering services in terms of the number of banquet attendees x . The profit functions for each of the possible Contractors in terms of x  are P a(x)=  ____________________________________________ and P b(x) =  ____________________________________________.​

• 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 Profit function, P(x) , for each of the two possible catering services in terms of the number of banquet attendees x .

The profit functions for each of the possible Contractors in terms of x  are

P _a(x)=  ____________________________________________ and
P _b(x) =  ____________________________________________.​