A farmer used to sell a carton of eggs for $2.50 each. At this price, the farmer used to sell an average of 3,500 cartons of eggs per month. When the farmer raised the price to $3.10, sales dropped to an average of 2,900 cartons of eggs per month. The farmer's fixed costs are $1,041.60 per month and the variable costs are $1.42 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 the farmer's monthly revenue function in terms of x R(x) = (C) Assume that the farmer's monthly cost function is linear. Express the farmer's monhtly cost function in terms of x. C(x) = (D) Find the farmer's monthly profit function in terms of x. P(x) = (E) What is the average number of cartons of eggs that would maximize the farmers's monthly profit? The optimal average number of cartons of eggs is x = (E) Suppose that during winter time x cannot be larger than 3000 cartons of eggs per month. What is the average number of cartons of eggs that would maximize the farmers's monthly profit during the winter? The optimal average number of cartons of eggs during the winter is x =