Explanation Given information: It is provided that the rate of change of production of the average worker at a factory is d p d t = 27 + 24 t − 3 t 2 . Formula used: The number of units produced is given by the integral of the rate of change of production, p ( t ) = ∫ d p d t d t Calculation: Consider the provided equation, d p d t = 27 + 24 t − 3 t 2 Use the formula of production to calculate the number of units produced as, p ( t ) = ∫ ( 27 + 24 t − 3 t 2 ) d t = ∫ ( 27 ) d t + ∫ ( 24 t ) d t + ∫ ( − 3 t 2 ) d t + C = 27 t + 24 t 2 2 − 3 ⋅ <

Mathematical Applications for the Management, Life, and Social Sciences

12th Edition

ISBN: 9781337625340

Author: Ronald J. Harshbarger, James J. Reynolds

Publisher: Cengage Learning

See similar textbooks

Concept explainers

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …

Videos

Question

Chapter 12, Problem 36RE

To determine

To calculate: The number of units the worker produce in an $8−$ hour shift where at a factory, the rate of change of production of an average worker is given by $dpdt=27+24t−3t2$ for $0≤t≤8$ and $p$ is the number of units the worker produces in $t$ hours.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 12, Problem 35RE

Chapter 12, Problem 37RE

Students have asked these similar questions

No chatgpt pls will upvote

Find an nfa that accepts the language L(aa (a + b)). Create and test the NFA in Jflap. Test the strings: aab, ab, aaaa, aaaab, baab, aa, abbbb, a, b, 1. Submit the Jflap diagram and the Jflap test cases. 4. Find an nfa that accepts the language L (aa* (a+b)).

CVE, AVM, AC, ¬SA¬ME A Fitch Style proof for this argument

Chapter 12 Solutions

Mathematical Applications for the Management, Life, and Social Sciences

Ch. 12.1 - 1. True or false: (a) (b) Ch. 12.1 - Prob. 2CP Ch. 12.1 - 1. If what is Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - Prob. 4E Ch. 12.1 - Prob. 5E Ch. 12.1 - Evaluate the integrals in Problems 5-28. Check...Ch. 12.1 - Prob. 7E Ch. 12.1 - Evaluate the integrals in Problems 5-28. Check...

Knowledge Booster

Learn more about

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

The number of units the worker produce in an 8 − hour shift where at a factory, the rate of change of production of an average worker is given by d p d t = 27 + 24 t − 3 t 2 for 0 ≤ t ≤ 8 and p is the number of units the worker produces in t hours.

Solution Summary: The author calculates the number of units the worker produces in an 8-hour shift by using the formula of production.

Concept explainers

Videos

To calculate: The number of units the worker produce in an $8−$ hour shift where at a factory, the rate of change of production of an average worker is given by $dpdt=27+24t−3t2$ for $0≤t≤8$ and $p$ is the number of units the worker produces in $t$ hours.

Want to see the full answer?

Chapter 12 Solutions