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In general, the profit function is the difference between the revenue and cost functions, P(x) = R(x) - C(x). Suppose the price-demand and cost functions for the production of cordless drills is given respectively by p = 143 - 0.03x and C(x) = 75,000 + 65x, where x is the number of cordless drills that are sold at a price of p dollars per drill and C(x) is the cost (in dollars) of producing x cordless drills. (a) Find the marginal cost function, MC(x). MC(x) = (b) Find the revenue, R(x), and marginal revenue, MR(x), functions. R(x) = MR(x) = (c) Find R'(1000) in dollars per drill. R'(1000) = dollars per drill Interpret the results. At a production level of 1000 cordless drills, revenue is ---Select--- v at a rate of the absolute value of R'(1000) dollars per drill. Find R'(4000) in dollars per drill. R'(4000) = dollars per drill Interpret the results. At a production level of 4000 cordless drills, revenue is -Select--- at a rate of the absolute value of R'(4000) dollars per drill. (d) Find the profit, P(x), and marginal profit, MP(x), functions. P(x) = MP(x) = (e) Find P'(1000) in dollars per drill. P'(1000) = dollars per drill Interpret the results. At a production level of 1000 cordless drills, profit is ---Select-- v at a rate of the absolute value of P'(1000) dollars per drill. Find P'(4000) in dollars per drill. P'(4000) = dollars per drill Interpret the results. At a production level of 4000 cordless drills, profit is ---Select--- v at a rate of the absolute value of P'(4000) dollars per drill.

In general, the profit function is the difference between the revenue and cost functions, P(x) = R(x) - C(x). Suppose the price-demand and cost functions for the production of cordless drills is given respectively by p = 143 - 0.03x and C(x) = 75,000 + 65x, where x is the number of cordless drills that are sold at a price of p dollars per drill and C(x) is the cost (in dollars) of producing x cordless drills. (a) Find the marginal cost function, MC(x). MC(x) = (b) Find the revenue, R(x), and marginal revenue, MR(x), functions. R(x) = MR(x) = (c) Find R'(1000) in dollars per drill. R'(1000) = dollars per drill Interpret the results. At a production level of 1000 cordless drills, revenue is ---Select--- v at a rate of the absolute value of R'(1000) dollars per drill. Find R'(4000) in dollars per drill. R'(4000) = dollars per drill Interpret the results. At a production level of 4000 cordless drills, revenue is -Select--- at a rate of the absolute value of R'(4000) dollars per drill. (d) Find the profit, P(x), and marginal profit, MP(x), functions. P(x) = MP(x) = (e) Find P'(1000) in dollars per drill. P'(1000) = dollars per drill Interpret the results. At a production level of 1000 cordless drills, profit is ---Select-- v at a rate of the absolute value of P'(1000) dollars per drill. Find P'(4000) in dollars per drill. P'(4000) = dollars per drill Interpret the results. At a production level of 4000 cordless drills, profit is ---Select--- v at a rate of the absolute value of P'(4000) dollars per drill.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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In general, the profit function is the difference between the revenue and cost functions, P(x) = R(x) - C(x). Suppose the price-demand and cost functions for the production of cordless drills is given respectively by p = 143 – 0.03x and C(x) = 75,000 + 65x, where x is the number of cordless drills that are sold at a price of p dollars per drill and C(x) is the cost (in dollars) of producing x cordless drills. (a) Find the marginal cost function, MC(x). MC(x) = (b) Find the revenue, R(x), and marginal revenue, MR(x), functions. R(x) = MR(x) = (c) Find R'(1000) in dollars per drill. R'(1000) = dollars per drill Interpret the results. At a production level of 1000 cordless drills, revenue is ---Select--- v at a rate of the absolute value of R'(1000) dollars per drill. Find R'(4000) in dollars per drill. R'(4000) = dollars per drill Interpret the results. At a production level of 4000 cordless drills, revenue is---Select-- v at a rate of the absolute value of R'(4000) dollars per drill. (d) Find the profit, P(x), and marginal profit, MP(x), functions. P(x) = MP(x) = (e) Find P'(1000) in dollars per drill. P'(1000) = dollars per drill Interpret the results. At a production level of 1000 cordless drills, profit is ---Select--- v at a rate of the absolute value of P'(1000) dollars per drill. Find P'(4000) in dollars per drill. P'(4000) = dollars per drill Interpret the results. At a production level of 4000 cordless drills, profit is ---Select- v at a rate of the absolute value of P'(4000) dollars per drill.
Transcribed Image Text:In general, the profit function is the difference between the revenue and cost functions, P(x) = R(x) - C(x). Suppose the price-demand and cost functions for the production of cordless drills is given respectively by p = 143 – 0.03x and C(x) = 75,000 + 65x, where x is the number of cordless drills that are sold at a price of p dollars per drill and C(x) is the cost (in dollars) of producing x cordless drills. (a) Find the marginal cost function, MC(x). MC(x) = (b) Find the revenue, R(x), and marginal revenue, MR(x), functions. R(x) = MR(x) = (c) Find R'(1000) in dollars per drill. R'(1000) = dollars per drill Interpret the results. At a production level of 1000 cordless drills, revenue is ---Select--- v at a rate of the absolute value of R'(1000) dollars per drill. Find R'(4000) in dollars per drill. R'(4000) = dollars per drill Interpret the results. At a production level of 4000 cordless drills, revenue is---Select-- v at a rate of the absolute value of R'(4000) dollars per drill. (d) Find the profit, P(x), and marginal profit, MP(x), functions. P(x) = MP(x) = (e) Find P'(1000) in dollars per drill. P'(1000) = dollars per drill Interpret the results. At a production level of 1000 cordless drills, profit is ---Select--- v at a rate of the absolute value of P'(1000) dollars per drill. Find P'(4000) in dollars per drill. P'(4000) = dollars per drill Interpret the results. At a production level of 4000 cordless drills, profit is ---Select- v at a rate of the absolute value of P'(4000) dollars per drill.
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