I really need help with this homwork problem its an practical application problem that i need to solve. i tried to solve but couldn't please help!

Premise - [A non - profit organization wants to do a dinner banquet/fundraiser for a good cause. It wants to decide which catering service to use between 2 different services, and raise as much money as possible.]

Part 1.

1. Catering company "A" has a fixed cost of $3000 and charges $20 per plate.

2. Catering company "B" has a fixed cost of $1500 and charges $30 per plate.

- For part 1: Write down the Cost function A(x) and B(x) assuming x is the demand, i.e. the number of people attending the fundraiser.

Part 2.

The price of a ticket that the company will charge is assumed to be linear (of the form "ax+b" where a and b are constants), based on the expected number of attendees (demand) x. If there are 200 attendees the price will be $80 per plate. If there are 300 attendees the price will be $70 per plate.

- For part 2 : Write down the price function p(x) using the information given.

Part 3.

Attendees are expected to give an average of $200 per person to the non-profit during the banquet.

- For part 3: Use this and the price function p(x) to find the Revenue function R(x) which will give the total revenue based on x people attending the benefitUsing the revenue function R(x) and the cost functions in part 1, find the overall profit function associated with using Catering company A (Let's call it f(x)), as well as the overall profit function associated with using Catering company B (Let's call it g(x)).

Part 4.

We wish to find the number of attendees x that would maximize profit if we were using Company A, and Company B.

- For part 4: a. Find the value x for which x is the profit is maximized for Company A. Use the second derivative test to confirm your answer. In addition, show a graph (feel free to use desmos for this) of the profit function for Company A and label the point at which the maximum occurs. Find the total profit at the point.

b. Find the value x for which x is the profit is maximized for Company B. Use the second derivative test to confirm your answer. In addition, show a graph (you can use desmos for this) of the profit function for Company A and label the point at which the maximum occurs. Find the total profit at the point.

c. Which company would you use to cater? Explain your decision verbally and mathematically.

Part 5.

We now change the premise of the story slightly. Suppose the Costs associated with catering service A and B now are charging money based on the square footage of the rental location (Let y be the variable associated to the square footage). They both are charging for every square foot above 10,000 square feet so that the new cost functions are given as follows:

C_A(x,y)=A(x)+(y-10000)^2 (This is the new cost function for company A, where A(x) was derived in part 1) C_B(x,y)=B(x)+(y-10000)^2 (Note in this we assume that the square footage of the rental location will be at least 10,000)

For part 5: a) Find the new Profit function corresponding to using Catering Service A. Then find the point q=(x,y) for which the profit is maximized, and use the second derivative test to confirm your answer is a maximum of the function. Find the total profit at the point q.

b) Find the new Profit function corresponding to using Catering Service B. Find the point s=(x,y) for which the profit is maximized, and use the second derivative test to confirm your answer is a maximum of the function. Find the profit at the point s.

c) Which Catering Service would you use in this situation? Explain verbally and/or mathematically.