(a) Suppose that a company's total cost (TC) of producing x thousand units of output is given by the function TC=2X^3+5 .

(a) Suppose that a company's total cost (TC) of producing x thousand units of output is given by the function TC=2X^3+5 . (MC=6X^2)

(b) The output in (a) is sold according to the demand equation p= 50 - 0.5x , where p is the price per unit. Find the total revenue (TR) function, where TR is price times quantity sold. Calculate the derivative of the TR function. Why does it give the marginal revenue (MR)? For this question, is it mean 50-0.5X*X? Or 50-0.5X*6X^2?

(c) Find the positive output x (rounded to 3 decimal places) at which MR=MC. This is mean I have to calculate both values of MC and MR?