A manufacturer produces a product at a cost of 22.80 per...

A manufacturer produces a product at a cost of $\$ 22.80$ per unit. The manufacturer has a fixed cost of $\$ 400.00$ per day. Each unit retails for $\$ 37.00$ Let $x$ represent the number of units produced in a 5 -day period. a. Write the total cost $C$ as a function of $x$ b. Write the revenue $R$ as a function of $x$ c. Write the profit $P$ as a function of $x .$ [Hint: The profit function is given by $P(x)=R(x)-C(x) .]$

A manufacturer produces a product at a cost of $\$ 22.80$ per unit. The manufacturer has a fixed cost of $\$ 400.00$ per day. Each unit retails for $\$ 37.00$ Let $x$ represent the number of units produced in a 5 -day period.
a. Write the total cost $C$ as a function of $x$
b. Write the revenue $R$ as a function of $x$
c. Write the profit $P$ as a function of $x .$ [Hint: The profit function is given by $P(x)=R(x)-C(x) .]$

Key Concepts

Linear Functions in Business Economics

Linear functions are commonly used in business economics to model relationships such as cost, revenue, and profit because they allow for straightforward interpretation of rate changes and scalability. This concept is crucial for predicting how changes in production levels directly influence financial outcomes.

Cost Function

The cost function represents the total cost incurred in production, which includes both fixed costs that remain constant regardless of production levels and variable costs that scale with the number of units produced. This function is essential for understanding how costs change as production increases and forms the basis for further financial analysis.

Revenue Function

The revenue function calculates the total income generated from selling a product by multiplying the selling price per unit by the number of units sold. It is fundamental in determining the income side of a business operation and is often modeled linearly for simplicity.

Profit Function

The profit function is obtained by subtracting the total costs from the total revenue. It measures the financial gain and is critical for evaluating business performance, guiding decision-making processes, and determining break-even points.

Transcript

Please give Ace some feedback