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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?Please solve for the marginal revenue function using the demand function: Q=1400-100pSuppose 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 marginal revenue from the 10th unit is given by the following function:- 2Q2 - 36 Find the marginal revenueA 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.The marginal revenue function for a manufacturer's is a of form (a)/(e^(q)+b) where a and b are constants. A)Derive the demand function. B)Analyze the features of function elements of a and b.
- 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. Derive and expression C(q) for the firm's total cost function.If the marginal revenue in dollars per unit for a month is given by MR= −0.04x + 36, find the total revenue function provided that R(0)= 25
- 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.The total revenue curve of a firm is R(q) = 40q − 12q2 and its average cost A(q) = 1/30 q2 − 12.85q + 20 + 400/q , ,where q is the firms output. Derive expressions for the firm's: (i) total cost function (ii) total profit functionFind the marginal revenue function for the demand function, Q=24-2P and evaluate at Q=10 .