A Fast-Food Restaurant Determines the Cost Model $C = 0.6 x + 5500,0 \leq x \leq 40000$

question 67

Multiple Choice

A fast-food restaurant determines the cost model, $C = 0.6 x + 5500,0 \leq x \leq 40000$ and revenue model, $R = \frac { 1 } { 30000 } \left( 55000 x - x ^ { 2 } \right)$ for $0 \leq x \leq 40000$ where x is the number of hamburgers sold. Determine the intervals on which the profit function is increasing and on which it is decreasing.

• A)The profit function is increasing on the interval \(( 18500,40000 )\) and decreasing on the interval \(( 0,18500 )\) .
• B)The profit function is increasing on the interval \(( 0,12500 )\) and decreasing on the interval \(( 12500,40000 )\) .
• C)The profit function is increasing on the interval \(( 0,18500 )\) and decreasing on the interval \(( 18500,40000 )\) .
• D)The profit function is increasing on the interval \(( 12500,40000 )\) and decreasing on the interval \(( 0,12500 )\) .
• E)The profit function is increasing on the interval \(( 0,5500 )\) and decreasing on the interval \(( 5500,40000 )\) .

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Definitions:

Per Capita GDP

A measure of the economic output of a country divided by its population, reflecting the average income per person.

GDP Deflator

An economic metric that converts output measured at current prices into constant-dollar gross domestic product, thereby indicating the level of inflation or deflation.

Population

The total number of individuals inhabiting a particular territory or living within a specified demographic boundary.

Economic Well-Being

A measure of the economic success and quality of life for individuals and nations, often evaluated through income levels, employment rates, and access to resources.