(a) Explanation Given information : It is given that a manufacturer estimates that profit on selling an item will be given by the function N = − p 2 + 14 p − 48 thousand dollars, when the price of each item is p dollars . Formula used : We use the quadratic formula, p = − b ± b 2 − 4 a c 2 a To solve any quadratic equation of the formula a p 2 + b p + c = 0 . Calculation : In given equation, N = − p 2 + 14 p − 48 , we have a = − 1 , b = 14 , c = − 48 So, using above quadratic formula: p = − 14 ± ( 14 ) 2 − 4 ( − 1 ) (b) To determine To calculate that which price results in the maximum profit and also that what will be the maximum profit. (c) To determine To guess the area of shaded reason as given in both below figures.

Student's Solution and Survival Manual for Calculus

7th Edition

ISBN: 9781524934040

Author: STRAUSS MONTY J, TODA MAGDALENA DANIELE, SMITH KARL J

Publisher: Kendall Hunt Publishing

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Question

Chapter 1, Problem 81SP

(a)

To determine

To calculate that for what value of p, the profit function N=−p2+14p−48 is a profitable operation.

(b)

To determine

To calculate that which price results in the maximum profit and also that what will be the maximum profit.

(c)

To determine

To guess the area of shaded reason as given in both below figures.

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Chapter 1, Problem 80SP

Chapter 1, Problem 82SP

Chapter 1 Solutions

Student's Solution and Survival Manual for Calculus

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Finding Local Maxima and Minima by Differentiation; Author: Professor Dave Explains;https://www.youtube.com/watch?v=pvLj1s7SOtk;License: Standard YouTube License, CC-BY

To calculate that for what value of p, the profit function N = − p 2 + 14 p − 48 is a profitable operation.

Solution Summary: The author explains that the profit function N=p2+14p48 is a profitable operation, and calculates the maximum profit at the vertex of the parabola.

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To calculate that for what value of p, the profit function N=−p2+14p−48 is a profitable operation.

To calculate that which price results in the maximum profit and also that what will be the maximum profit.

To guess the area of shaded reason as given in both below figures.

Want to see the full answer?

Chapter 1 Solutions