The price-demand equation and the cost function for the production of TVs are given, respectively, by =800020 and ()=125000+40 where is the number of TVs that can be sold at a price of per TV and () is the total cost (in dollars) of producing TVs. a) Express (solve) the price as a function of the demand , and find the domain of this function. b) Find the marginal cost, and marginal average cost functions. c) Find the revenue function, (), and state its domain.(Hint: ()=) d) Find the marginal revenue, and marginal average revenue functions. e) Find (3500) and (4500) and interpret these quantities. f) Graph the cost function and the revenue function on the same coordinate system by letting takes values in the interval you found in part (a). Then, find the break-even points, and indicate regions of loss and profit using intervals. (Use Excel) g) Using the cost function given above, and the revenue function you found in part (c), construct the profit function, (), by letting takes values in the interval you found in part (a) (Use Excel). Then find the marginal profit function algebraically. h) Find (4000) using the definition of the limit, and then interpret the result. Lastly, compare (4000), i.e. the marginal profit at 4000, with the actual change in profit by considering the difference (4001) (4000). What do you think? (Use Excel) (Hint: Review "Module 4-Excel Applications, Example 3")