Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 7 - Algebra: Graphs, Functions, and Linear Systems - 7.3 Systems of Linear Equations in Two Variables - Exercise Set 7.3 - Page 445: 55

Answer

See below:

Work Step by Step

(a) The company’s cost and revenue functions are given as \[C\left( x \right)\]and \[R\left( x \right)\], respectively. The profit function \[P\left( x \right)\] of the company can be found by subtracting the cost function from the revenue function: \[P\left( x \right)=R\left( x \right)-C\left( x \right)\] Substitute the values for cost and revenue function. \[\begin{align} & P\left( x \right)=50x-\left( 10,000+30x \right) \\ & =20x-10,000 \end{align}\] Thus, the obtained revenue function is\[P\left( x \right)=20x-10,000\]. (b) The profit function \[P\left( x \right)\] of the company can be found by subtracting the cost function from the revenue function. \[P\left( x \right)=R\left( x \right)-C\left( x \right)\] Thus, apply the above formula: \[\begin{align} & P\left( x \right)=50x-\left( 10,000+30x \right) \\ & =20x-10,000 \end{align}\] Here, \[x\] is the number of units produced and sold. Therefore, substitute \[10,000\]for\[x\]: \[\begin{align} & P\left( 10,000 \right)=20\left( 10,000 \right)-10,000 \\ & =200,000-10,000 \\ & =\$190,000\end{align}\] Thus, the profit of the company is\[\$190,000\].
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