Question

The marketing department of a company estimates that the demand for a product is given by $p=100-0.0001 x$, where $p$ is the price per unit and $x$ is the number of units. The cost $C$ of producing $x$ units is given by $C=350,000+30 x$, and the profit $P$ for producing and selling $x$ units is given by $P=R-C=x p-C$ Sketch the graph of the profit function and estimate the number of units that would produce a maximum profit. Verify your estimate using a graphing utility.

          The marketing department of a company estimates that the demand for a product is given by $p=100-0.0001 x$, where $p$ is the price per unit and $x$ is the number of units. The cost $C$ of producing $x$ units is given by $C=350,000+30 x$, and the profit $P$ for producing and selling $x$ units is given by
$P=R-C=x p-C$
Sketch the graph of the profit function and estimate the number of units that would produce a maximum profit. Verify your estimate using a graphing utility.

Added by Michael S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Vishal Parmar

09/10/2022

Step 1

### Step 1: Express the Revenue Function The revenue $ R $ is given by the product of the price per unit $ p $ and the number of units $ x $. Given the demand function $ p = 100 - 0.0001x $, we can write the revenue function as: \[ R = x \cdot p = x \cdot Show more…

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The marketing department of a company estimates that the demand for a product is given by $p=100-0.0001 x$, where $p$ is the price per unit and $x$ is the number of units. The cost $C$ of producing $x$ units is given by $C=350,000+30 x$, and the profit $P$ for producing and selling $x$ units is given by $P=R-C=x p-C$ Sketch the graph of the profit function and estimate the number of units that would produce a maximum profit. Verify your estimate using a graphing utility.