(a) The cost to produce the Rolls-Royce can be estimated at $200 million of fixed costs (factory maintenance, equipment leasing, labor, etc.) plus $110000 per vehicle. Write profit P, in thousands of dollars, as a formula involving the price per vehicle, p (in thousands of dollars), and q the quantity of vehicles produced: P = The profit associated with the production and sale of a product is the difference between the product's revenue and the cost to produce it. (b) In 2011, Rolls-Royce sold 3538 cars at an average price per vehicle of $200 thousand. Assume that the demand for these vehicles is proportional to the price, p, in thousands of dollars, and write a formula for the quantity of Rolls-Royce vehicles demanded as a function of p. q= D(p) 17.69p (c) Use the demand model from part (b) to rewrite your profit formula from part (a) so that P is a function of only p. P(p) =

(a) The cost to produce the Rolls-Royce can be estimated at $200 million of fixed costs (factory maintenance, equipment leasing, labor, etc.) plus $110000 per vehicle. Write profit P, in thousands of dollars, as a formula involving the price per vehicle, p (in thousands of dollars), and q the quantity of vehicles produced: P = The profit associated with the production and sale of a product is the difference between the product's revenue and the cost to produce it. (b) In 2011, Rolls-Royce sold 3538 cars at an average price per vehicle of $200 thousand. Assume that the demand for these vehicles is proportional to the price, p, in thousands of dollars, and write a formula for the quantity of Rolls-Royce vehicles demanded as a function of p. q= D(p) 17.69p (c) Use the demand model from part (b) to rewrite your profit formula from part (a) so that P is a function of only p. P(p) =

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

The
profit associated with the production and sale of a product is the difference between the product's revenue and the cost to produce it.
(a) The cost to produce the Rolls-Royce can be estimated at $200 million of fixed costs (factory maintenance, equipment leasing, labor, etc.) plus
$110000 per vehicle. Write profit P, in thousands of dollars, as a formula involving the price per vehicle, p (in thousands of dollars), and q the quantity of
vehicles produced:
P =
(b) In 2011, Rolls-Royce sold 3538 cars at an average price per vehicle of $200 thousand. Assume that the demand for these vehicles is proportional to
the price, p, in thousands of dollars, and write a formula for the quantity of Rolls-Royce vehicles demanded as a function of p.
q = D(p) = 17.69p
(c) Use the demand model from part (b) to rewrite your profit formula from part (a) so that P is a function of only p.
P(p) =
(d) At what price does the model predict break even is attained?
Price:
thousand dollars
(e) What is the value of profit at the vertex of the quadratic? [Note: This is not the company's maximum profit! Why?]
Maximum:
thousand dollars

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