In an economic enterprise, the total amount T that is produced is a function of the amount n of a given input used in the process of production. For example, the yield of a crop depends on the amount of fertilizer used, and the number of widgets manufactured depends on the number of workers. Because of the law of diminishing returns, a graph for T commonly has an inflection point followed by a maximum, so a cubic model may be appropriate. In this exercise we use the model shown below, with n measured in thousands of units of input and T measured in thousands of units of product.T = −2n3 + 3n2 + n(a) Make a graph of T as a function of n. Include values of n up to 1.5 thousand units. (b) Express using functional notation the amount produced if the input is 1.02 thousand units. (Round your answer to two decimal places.)T( )Calculate that value. (Round your answer to two decimal places.) thousand units(c) Find the approximate location of the inflection point. (Round your answers to one decimal place.)(n, T) = ( , )Explain what it means in practical terms.(d) What is the maximum amount produced? (Round your answer to two decimal places.)T = thousand units

(a) The graph of the function is as follows: (b) Here, T(1.02)=-2(1.02)3+3(1.02)2+1.02…

Answered: In an economic enterprise, the total…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 98E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

See similar textbooks

Related questions

Concept explainers

Question

In an economic enterprise, the total amount T that is produced is a function of the amount n of a given input used in the process of production. For example, the yield of a crop depends on the amount of fertilizer used, and the number of widgets manufactured depends on the number of workers. Because of the law of diminishing returns, a graph for T commonly has an inflection point followed by a maximum, so a cubic model may be appropriate. In this exercise we use the model shown below, with n measured in thousands of units of input and T measured in thousands of units of product.

T = −2n³ + 3n² + n

(a) Make a graph of T as a function of n. Include values of n up to 1.5 thousand units.

(b) Express using functional notation the amount produced if the input is 1.02 thousand units. (Round your answer to two decimal places.)
T( )

Calculate that value. (Round your answer to two decimal places.)
thousand units

(c) Find the approximate location of the inflection point. (Round your answers to one decimal place.)

(n, T)

( , )

Explain what it means in practical terms.

(d) What is the maximum amount produced? (Round your answer to two decimal places.)
T = thousand units

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Differential Equation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions