Pearl Ltd. intends to manufacture and market mechanical weighing scales. Their research department has derived the price-demand equation and the cost function, respectively as x = 6200 - 50p and C(x) = 7400 + 70x where x is the number of scales that can be sold at Sp per unit and C(x) represents the total cost of producing x scales. (a) Express the price p as a function of the demand x. Find the domain of this function. (b) Find the exact cost of producing the 45th scale.
Pearl Ltd. intends to manufacture and market mechanical weighing scales. Their research department has derived the price-demand equation and the cost function, respectively as x = 6200 - 50p and C(x) = 7400 + 70x where x is the number of scales that can be sold at Sp per unit and C(x) represents the total cost of producing x scales. (a) Express the price p as a function of the demand x. Find the domain of this function. (b) Find the exact cost of producing the 45th scale.
Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
14th Edition
ISBN:9781305506381
Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Chapter9: Applications Of Cost Theory
Section: Chapter Questions
Problem 3E
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MARGINAL ANALYSIS
![Pearl Ltd. intends to manufacture and market mechanical weighing scales. Their research
department has derived the price-demand equation and the cost function, respectively as
x = 6200 - 50p and C(x) = 7400 + 70x
where x is the number of scales that can be sold at Sp per unit and C(x) represents the total
cost of producing x scales.
(a) Express the price p as a function of the demand x. Find the domain of this function.
(b) Find the exact cost of producing the 45th scale.
(c) Find the marginal cost function and use it to approximate the cost of producing the 45th
scale.
(d) Determine the Revenue, R(x) and Profit, P(x) functions.
(e) Find the marginal revenue at production levels of 2800 and 3500 scales. Give an
interpretation for both results.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd8f34c27-d547-42cf-8513-49967d562251%2F8b7d09b7-28cd-40b6-bab5-5a9a3349bc81%2Fg7a7ajr_processed.png&w=3840&q=75)
Transcribed Image Text:Pearl Ltd. intends to manufacture and market mechanical weighing scales. Their research
department has derived the price-demand equation and the cost function, respectively as
x = 6200 - 50p and C(x) = 7400 + 70x
where x is the number of scales that can be sold at Sp per unit and C(x) represents the total
cost of producing x scales.
(a) Express the price p as a function of the demand x. Find the domain of this function.
(b) Find the exact cost of producing the 45th scale.
(c) Find the marginal cost function and use it to approximate the cost of producing the 45th
scale.
(d) Determine the Revenue, R(x) and Profit, P(x) functions.
(e) Find the marginal revenue at production levels of 2800 and 3500 scales. Give an
interpretation for both results.
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