Let $ x $ be the number of units (in thousands) that a company produces and let $ p(x) $ be the profit (in tens of thousands of dollars). The following table gives the profit for different levels of production.\[\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|}\hlinex & 2 & 4 & 6 & 8 & 10 & 12 & 14 & 16 & 18 & 20 \\\hlinep(x) & 0.6 & 2.8 & 6.7 & -12.2 & -16.6 & -23.7 & -27.9 & -37.7 & -45.2 & -58.4 \\\hline\end{array}\]Use the quadratic regression program to find a mathematical model for $ p(x) $.\[ p(x) = -0.4x^2 + 5.3x - 24.5 \]

From the given information, x x2 p(x) 2 4 0.6 4 16 -2.8 6 36 -6.7 8 64 -12.2 10 100 -16.6 12 144 -23.7 14 196 -27.9 16 256 -37.7 18 324 -45.2 20 400 -58.4Excel Procedure: Enter X, X2 and Y data in Excel Go to Data Click on Data Analysis> ‘Regression’. Select Y under ‘Input Y Range’. Select X, X2 under ‘Input X Range’. Click on ‘OK’. Output: From the output, p(x)=1.765-0.707x-0.111x2

Math

Statistics

Let z be the number of units (in thousands) that a company produces and let p(x) be the profit (in tens of thousands of The following table gives the profit for different levels of production. I 246 8 10 12 14| 16 18 20 p(x)0.6-2.8-6.7-12.2-16.6-23.7-27.9-37.7-45.2-58.4 quadratic regression program to find a mathematical model for p(x).

Let z be the number of units (in thousands) that a company produces and let p(x) be the profit (in tens of thousands of The following table gives the profit for different levels of production. I 246 8 10 12 14| 16 18 20 p(x)0.6-2.8-6.7-12.2-16.6-23.7-27.9-37.7-45.2-58.4 quadratic regression program to find a mathematical model for p(x).

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Let $ x $ be the number of units (in thousands) that a company produces and let $ p(x) $ be the profit (in tens of thousands of dollars). The following table gives the profit for different levels of production.

\[
\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|}
\hline
x & 2 & 4 & 6 & 8 & 10 & 12 & 14 & 16 & 18 & 20 \\
\hline
p(x) & 0.6 & 2.8 & 6.7 & -12.2 & -16.6 & -23.7 & -27.9 & -37.7 & -45.2 & -58.4 \\
\hline
\end{array}
\]

Use the quadratic regression program to find a mathematical model for $ p(x) $.

\[ p(x) = -0.4x^2 + 5.3x - 24.5 \]

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