Let a linear cost function C(x) = 21.95 + 1400 and a linear revenue function R(x) = 20x. What is the marginal cost? What is the marginal revenue? Write the profit function P(x). What is the marginal profit
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Let a linear cost function C(x) = 21.95 + 1400 and a linear revenue function R(x) = 20x. What is the marginal cost? What is the marginal revenue? Write the profit function P(x). What is the marginal profit?
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- Suppose the marginal cost of producing x units of a product is given by: MC=4x+50 And the marginal revenue is given by: MR = 500 And the cost of the production and sale of 10 units is $1000. What is the profit function for this product ?The total revenue curve of a firm is R(q) = 40q − 12q2 and its average cost A(q) = 1/30q2 − 12.85q + 20 + 400/q. The total cost function is C(q) = 1/30q3 – 12.85q2 + 20q + 400 . The profit function is Π(q)= –1/30q3 + 0.85q2 + 20q – 400 (i) Is the rate of change of profit increasing or decreasing when the output level of the firm is 10 units?A firm has a cost function of C = 1000 + 20Q + 1/10Q2a) Estimate the firm’s demand function. You may assume that the slope is a wholenumber, and the intercept is a multiple of 10. b) Find the firm’s revenue function. You do not need to draw it. c) Find the marginal revenue function, and draw it on a copy of the graph. d) Find and draw the marginal cost function.e) Use your results from parts (c) and (d) to find the profit-maximising level of output.(3 marks)f) Find the market price at this level of output.
- A firm's demand and total cost function are given by the expression: P = 20 - Q/2 (1) TC = 0.5Q2 + 36 (2) Where P is price per unit in £ TC = total cost in £ Q is quantity demanded and produced. Find the profit-maximising level of output using the profit function and calculate how much profit is made at this output level.The total revenue curve of a firm is R(q) = 40q − 12q2 and its average cost A(q) = 1/30q2 − 12.85q + 20 + 400/q. The total cost function is C(q) = 1/30q3 – 12.85q2 + 20q + 400 . The profit function is Π(q)= –1/30q3 + 0.85q2 + 20q – 400 (i) Determine the level of output for which the firm’s profit is maximized. (ii) What is the firm's maximum profit?Sergio Lopez is a publisher of Latin American poetry. His fixed cost is $525, and the cost to produce each individual copy of his book is $3.50. Currently, Sergio is selling these books for $6 each. So far this year, he has produced x a. Write a linear cost function C for Sergio’s book production, in terms of x. b. Find the linear revenue function R for selling x copies of the book. Remember that P(x) = (price)x. c. Use and 1b. to determine the profit function P for selling x books. Write the formula in simplified form. d.Use your answer for 1c to determine the profit, in dollars, for selling 300 books.
- Given Cost and Price (demand) functions C(q)=120q+45000 and p(q)=−2.8q+900, what is the marginal revenue when costs are $80,000? The marginal revenue is ____dollars per item.The total cost function of a firm producing Jeans is TC = 0.5Q3− 15Q2 + 175Q + 100, where Q is output. a.What are the total variable cost (TVC) and the total fixed cost (TFC) in this case? b.The average cost is given by AC = TC/Q, the average variable cost is AVC = TVC/Q and the average fixed cost is AFC = TFC/Q. Find the AC, AVC and AFC functions. c. If the marginal cost is MC = 3(0.5)Q2 - 2(15)Q + 175, then roughly sketch the graph of MC, AVC and AC (If you know how to use Excel, then you can get more accurate graphs). What relationship do you observe between the three cost curves?It costs a coat manufacturer $8750 to make 125 coats and it costs $6500 to make 80 coats. Each coat is sold for $250. a. How much is the marginal cost? Round to two decimal places if rounding is necessary. Do not enter a fraction. There is a $ sign next to the answer box, so do not type a $ sign in your answer. Only type a number (do not type any units on your answer). $ b. What is the slope of the Profit function, P(x)? Round to two decimal places if rounding is necessary. Do not enter a fraction. There is a $ sign next to the answer box, so do not type a $ sign in your answer. Only type a number (do not type any units on your answer). $ c. How many coats must be sold in order to break even? Round to the nearest whole number if rounding is necessary. Do not enter a fraction. Only type a whole number (do not type any units on your answer).
- Would a cost function of 0 mean a linear line of supply curve? For example if 10 firms are on the market selling 10 goods and the cost function is 0?Suppose a company's revenue function is given by R(q)=−q3+400q2R(q)=-q3+400q2 and its cost function is given by C(q)=550+12qC(q)=550+12q, where qq is hundreds of units sold/produced, while R(q)R(q) and C(q)C(q) are in total dollars of revenue and cost, respectively.A) Find a simplified expression for the marginal profit function. (Be sure to use the proper variable in your answer.) MP(q)=MP(q)= B) How many items (in hundreds) need to be sold to maximize profits? Answer: hundred units must be sold. (Round to two decimal places.)The total revenue curve of a firm is R (q) = 40q - 12q2 and its average cost A(q) = 1/30q2 - 12.85q +20 + 400/q, where q is the firm's output. (1) Derive and expression C(q) for the firm's total cost function.