A farmer used to sell a carton of eggs for $2.50 each. At this price, the farmer used to sell an average of 2,500 cartons of eggs per month. When the farmer raised the price to $3.20, sales dropped to an average of 1,800 cartons of eggs per month. The farmer's fixed costs are $2,966.60 per month and the variable costs are $0.83 per carton of eggs. Answer the following questions:

(A) Assume that the relationship between the price of a carton of eggs p and the demand for cartons of eggs x is linear. Express p as a function of x

p=

(B) Find thefarmer's monthly revenue function in terms of x

R(x)=

(C) Assume that thefarmer's monthly cost function is linear. Express thefarmer's monhtly cost function in terms of x.

C(x)=

(D) Find thefarmer's monthly profit function in terms of x.

P(x)=