### Cost Function and Marginal Analysis#### Problem StatementThe cost, in thousands of dollars, of airing $ x $ television commercials during a sports event is given by:\[ C(x) = 150 + 2.600x - 0.06x^2. \]#### Questions**(a) Find the marginal cost function $ C'(x) $.**\[ C'(x) = \text{(Enter marginal cost function here)} \]**(b) Use the marginal cost to approximate the cost to air the 5th commercial. Convert your answer to dollars.**The cost to air the 5th commercial is approximately $\boxed{\text{(enter approximate cost here)}}$ dollars.**(c) What is the exact cost to air the 5th commercial? Convert your answer to dollars.**The exact cost to air the 5th commercial is $\boxed{\text{(enter exact cost here)}}$ dollars.#### Explanation:- **Part (a):** Calculate the marginal cost function, which is the derivative of the cost function. This represents the cost change with respect to the number of commercials aired.- **Part (b):** Use the marginal cost function to estimate the cost of the additional (5th) commercial. This approximation is common in economic analysis to simplify calculations.- **Part (c):** Compute the exact cost of airing the 5th commercial by evaluating the difference in cost between airing 5 and 4 commercials.This exercise involves differentiation and basic cost analysis, core concepts in calculus and economics.

Marginal cost, C'(x) = change in total cost / change in quantity = δ(C)δx

The cost, in thousands of dollars, of airing x television commercials during a sports event is given by C(x) = 150 + 2,600x – 0.06x². (a) Find the marginal cost function C'(x). C'(x) = (b) Use the marginal cost to approximate the cost to air the 5th commercial. Convert your answer to dollars. The cost to air the 5th commercial is approximately × dollars. (c) What is the exact cost to air the 5th commercial? Convert your answer to dollars. The exact cost to air the 5th commercial is × dollars.

The cost, in thousands of dollars, of airing x television commercials during a sports event is given by C(x) = 150 + 2,600x – 0.06x². (a) Find the marginal cost function C'(x). C'(x) = (b) Use the marginal cost to approximate the cost to air the 5th commercial. Convert your answer to dollars. The cost to air the 5th commercial is approximately × dollars. (c) What is the exact cost to air the 5th commercial? Convert your answer to dollars. The exact cost to air the 5th commercial is × dollars.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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