The text presents a problem related to the production of table saws, involving both a price-demand equation and a cost function.**Price-Demand Equation**:The equation given for the demand is:\[ x = 6,000 - 20p \]Here, $ x $ represents the number of saws that can be sold at a price of $ \$p $ per saw.**Cost Function**:The cost function is expressed as:\[ C(x) = 98,000 + 70x \]This equation represents the total cost (in dollars) of producing $ x $ saws.**Problem (Part A)**:The task is to express the price $ p $ as a function of the demand $ x $, and to find the domain of this function.To solve Part A, we need to rearrange the price-demand equation to solve for $ p $:\[ x = 6,000 - 20p \]\[ 20p = 6,000 - x \]\[ p = \frac{6,000 - x}{20} \]Thus, the price function is:\[ p = \frac{6,000 - x}{20} \]Further, to determine the domain of this function, consider that $ x $ must be a non-negative number ($ x \geq 0 $), and cannot exceed 6,000 to keep the price non-negative. Therefore, the domain is:\[ 0 \leq x \leq 6,000 \]

Given the price-demand function x=6000-20p where x is the number of saws that can be solved at…

The price-demand equation and the cost function for the production of table saws are given, respectively, by x= 6,000 – 20p and C(x) = 98,000 + 70x, where x is the number of saws that can be sold at a price of $p per saw and C(x) is the total cost (in dollars) of producing x saws. Complete parts (A) through (I) below. (A) Express the price p as a function of the demand x, and find the domain of this function. The price function is p=

The price-demand equation and the cost function for the production of table saws are given, respectively, by x= 6,000 – 20p and C(x) = 98,000 + 70x, where x is the number of saws that can be sold at a price of $p per saw and C(x) is the total cost (in dollars) of producing x saws. Complete parts (A) through (I) below. (A) Express the price p as a function of the demand x, and find the domain of this function. The price function is p=

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

The text presents a problem related to the production of table saws, involving both a price-demand equation and a cost function.

**Price-Demand Equation**:
The equation given for the demand is:
\[ x = 6,000 - 20p \]

Here, $ x $ represents the number of saws that can be sold at a price of $ \$p $ per saw.

**Cost Function**:
The cost function is expressed as:
\[ C(x) = 98,000 + 70x \]

This equation represents the total cost (in dollars) of producing $ x $ saws.

**Problem (Part A)**:
The task is to express the price $ p $ as a function of the demand $ x $, and to find the domain of this function.

To solve Part A, we need to rearrange the price-demand equation to solve for $ p $:
\[ x = 6,000 - 20p \]
\[ 20p = 6,000 - x \]
\[ p = \frac{6,000 - x}{20} \]

Thus, the price function is:
\[ p = \frac{6,000 - x}{20} \]

Further, to determine the domain of this function, consider that $ x $ must be a non-negative number ($ x \geq 0 $), and cannot exceed 6,000 to keep the price non-negative. Therefore, the domain is:
\[ 0 \leq x \leq 6,000 \]

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