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The cost, in dollars, of producing a units of a certain item is given by C (x) = 0.04x3 – 5æ + 350. (a) Find the marginal cost function. MC (x) = (b) Find the marginal cost when 50 units of the item are produced. The marginal cost when 50 units are produced is $ Number (c) Find the actual cost of increasing production from 50 units to 51 units. The actual cost of increasing production from 50 units to 51 units is $ Number

The cost, in dollars, of producing a units of a certain item is given by C (x) = 0.04x3 – 5æ + 350. (a) Find the marginal cost function. MC (x) = (b) Find the marginal cost when 50 units of the item are produced. The marginal cost when 50 units are produced is $ Number (c) Find the actual cost of increasing production from 50 units to 51 units. The actual cost of increasing production from 50 units to 51 units is $ Number

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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the learning modules. Introduction to Calculus in Economics (continued): In the previous Problem Set question, we started looking at the cost function C (x), the cost of a firm producing x items. An important microeconomics concept is the marginal cost, defined in (non-mathematical introductory) economics as the cost of producing one additional item. If the current production level is x items with cost C (x), then the cost of computing h additionial items is C (x + h). The average cost of those h items is (C(x+h)-C(x)) As we analyze the cost of just the last item produced, this can be made into a mathematical model by taking the limit as h → 0, i.e. the derivative C' (x). Use this function in the model below for the Marginal Cost function MC (x). Problem Set question: The cost, in dollars, of producing x units of a certain item is given by C (x) = 0.04x³ – 5x + 350. (a) Find the marginal cost function. MC (x) = (b) Find the marginal cost when 50 units of the item are produced. The marginal cost when 50 units are produced is $ Number (c) Find the actual cost of increasing production from 50 units to 51 units. The actual cost of increasing production from 50 units to 51 units is $ Number
Transcribed Image Text:the learning modules. Introduction to Calculus in Economics (continued): In the previous Problem Set question, we started looking at the cost function C (x), the cost of a firm producing x items. An important microeconomics concept is the marginal cost, defined in (non-mathematical introductory) economics as the cost of producing one additional item. If the current production level is x items with cost C (x), then the cost of computing h additionial items is C (x + h). The average cost of those h items is (C(x+h)-C(x)) As we analyze the cost of just the last item produced, this can be made into a mathematical model by taking the limit as h → 0, i.e. the derivative C' (x). Use this function in the model below for the Marginal Cost function MC (x). Problem Set question: The cost, in dollars, of producing x units of a certain item is given by C (x) = 0.04x³ – 5x + 350. (a) Find the marginal cost function. MC (x) = (b) Find the marginal cost when 50 units of the item are produced. The marginal cost when 50 units are produced is $ Number (c) Find the actual cost of increasing production from 50 units to 51 units. The actual cost of increasing production from 50 units to 51 units is $ Number
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