Question

The total costs, in dollars, of producing a certain product are represented by C(x)=3,840+6(1,760-80x) where x is the price, in dollars, of the product. The total revenue, in dollars, from the sale of the product is represented by R(x)=x(1,760-80x), where x is the price, in dollars, of the product.

Which expression represents the total profit in dollars?

A. C(x) + R(x)
B. C(x) - R(x)
C. R(x) + C(x)
D. C(x)/R(x)

Answer 1

Total profit for the product is calculated by subtracting total costs from total revenue, which is represented by the formula R(x) - C(x), corresponding to answer option B.

Step-by-step explanation:

In the context of business and economics, profit is calculated by subtracting total costs from total revenue. Using the functions provided, the total cost (C(x)) of producing a product is C(x) = 3,840 + 6(1,760 - 80x), and the total revenue (R(x)) from selling the product is expressed as R(x) = x(1,760 - 80x). The total profit, therefore, is the total revenue minus the total costs, represented by R(x) - C(x).

To calculate the profit, you simply take the revenue formula and subtract the cost formula from it. Thus, the answer to the question is option B, represented by R(x) - C(x).

Answer 2

Step-by-step explanation:

The total profit is determined by subtracting the total cost from the total revenue.

In this case, the expression that represents the total profit is given by:

B. C(x) - R(x)

Step-by-step explanation:

1. The total cost function is represented by C(x) = 3,840 + 6(1,760 - 80x), where x is the price of the product.

2. The total revenue function is represented by R(x) = x(1,760 - 80x), where x is the price of the product.

3. To find the total profit, we subtract the total cost from the total revenue. This can be represented by C(x) - R(x).

4. By substituting the expressions for C(x) and R(x) into the expression for total profit, we get:

(3,840 + 6(1,760 - 80x)) - (x(1,760 - 80x))

5. Simplifying this expression further will give us the final equation for total profit.

Therefore, the expression that represents the total profit in dollars is B. C(x) - R(x).