The Marketing Department of a Company Estimates That the Demand $p = 180 - 0.0001 x,$

question 37

Multiple Choice

The marketing department of a company estimates that the demand for a product is given by $p = 180 - 0.0001 x,$ where $p$ is the price per unit and $x$ is the number of units. The cost $C$ of producing $x$ units is given by $C = 450,000 + 50 x,$ 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.

• A)690,000 units
• B)650,000 units
• C)610,000 units
• D)710,000 units
• E)580,000 units

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Definitions:

Prediction Interval

An estimate of an interval in which future observations will fall, with a certain probability, given what has already been observed.

Simple Linear Regression

A statistical method used to model the relationship between a single independent variable and a dependent variable by fitting a linear equation to observed data.

T-Table Values

Critical values used in t-tests that determine the thresholds for significance based on the sample size and desired confidence level.

Confidence Level

The percentage that expresses the degree of certainty in the reliability of a confidence interval.