A company produces x units of a product per month, were R(x) represents the total revenue and C(x) represents the total cost. The profit is calculated by taking the difference between revenue and cost, P(x)=R(x)-C(x). What is the total profit for the given functions? R(x)=350x-125 C(x)=175x-80
The correct answer and explanation is:
To calculate the total profit for the given functions, we use the profit formula: P(x)=R(x)−C(x)P(x) = R(x) – C(x)
Where:
- R(x)R(x) is the total revenue: R(x)=350x−125R(x) = 350x – 125
- C(x)C(x) is the total cost: C(x)=175x−80C(x) = 175x – 80
Substituting these into the profit equation: P(x)=(350x−125)−(175x−80)P(x) = (350x – 125) – (175x – 80)
Now, let’s simplify the equation: P(x)=350x−125−175x+80P(x) = 350x – 125 – 175x + 80
Combine like terms: P(x)=(350x−175x)+(−125+80)P(x) = (350x – 175x) + (-125 + 80) P(x)=175x−45P(x) = 175x – 45
Thus, the total profit function is: P(x)=175x−45P(x) = 175x – 45
Explanation:
- Understanding the Profit Function: The total profit function, P(x)P(x), represents how much profit a company makes when producing xx units of a product. The profit is the difference between the revenue (R(x)R(x)) and the cost (C(x)C(x)) of producing those units.
- Revenue Function: The revenue function R(x)=350x−125R(x) = 350x – 125 suggests that for each unit sold, the company earns 350 units of currency. However, there is a fixed cost (or adjustment) of 125 that reduces the overall revenue.
- Cost Function: The cost function C(x)=175x−80C(x) = 175x – 80 implies that the company incurs a cost of 175 units of currency for each unit produced, with a fixed cost of 80.
- Profit Calculation: By subtracting the cost from the revenue, we get the profit. The simplified result, P(x)=175x−45P(x) = 175x – 45, shows that for every unit produced, the company gains a profit of 175 units of currency, minus a fixed cost of 45 units.
Therefore, the total profit function is P(x)=175x−45P(x) = 175x – 45, and this function will give the total profit based on the number of units produced.