Final answer:
To calculate the marginal revenue (MR) and profit functions, we need to find the derivative of the total revenue and total cost functions.
Step-by-step explanation:
To calculate the marginal revenue (MR) and profit functions, we need to find the derivative of the total revenue and total cost functions. The total revenue function is TR(x) = xP(x), where P(x) is the price function. From the given information, we have the quantity and total revenue values for different quantities. Using these values, we can find the price function using the formula P(x) = TR(x)/x.
Now, to find the marginal revenue function, we take the derivative of the total revenue function with respect to x, which gives us MR(x) = P(x) + xP'(x). We can substitute the price function into the MR(x) equation to get MR(x) = TR(x)/x + xP'(x) = TR(x)/x + x(P(x)/x) = TR(x)/x + P(x).
Next, to find the profit function, we subtract the cost function C(x) from the total revenue function TR(x). The profit function is given by Profit(x) = TR(x) - C(x). From the given cost function, we can substitute the values of TR(x) and C(x) into the profit function to get Profit(x) = (TR(x) - C(x)).