Question

Show Examples

The revenue for a business, as a function oflunits produced, x, is shown below by R(x). C(x) represents
the cost of producing x units. Calculate the profit function and then determine how many units must be
produced for the business to make a profit of $636.
R(x) = 22x
C(x) = 10x +984
Answer Attempt 1 out of 2
The revenue function.
The cost function.

Answer 1

The profit function is P(x) = 12x - 984, and to achieve a profit of $636, the business must produce 135 units.

Step-by-step explanation:

To calculate the profit function, we subtract the cost function, C(x), from the revenue function, R(x). The revenue function given is R(x) = 22x, and the cost function is C(x) = 10x + 984.

The profit function P(x) can be calculated as follows:

P(x) = R(x) - C(x)

P(x) = 22x - (10x + 984)

P(x) = 22x - 10x - 984

P(x) = 12x - 984

To find out how many units must be produced to make a profit of $636, we set P(x) equal to 636 and solve for x:

636 = 12x - 984

12x = 636 + 984

12x = 1620

x = 135

Therefore, the business must produce 135 units to achieve a profit of $636.