Question

A fast-food restaurant has a cost of production C (x) = 13x + 147 and a revenue function R(x) = 6x. When does the company start to turn a profit?

Answer 1

The restaurant starts to turn a profit when it sells 21 units of its product.

Step-by-step explanation:

A fast-food restaurant starts to turn a profit when its revenue exceeds its cost of production. In this case, the revenue function is given by R(x) = 6x and the cost of production function is C(x) = 13x + 147. To find when the restaurant starts to turn a profit, we need to find the point of intersection between the revenue and cost functions.

1. Set the revenue function equal to the cost function: 6x = 13x + 147.
2. Solve for x: 13x - 6x = 147, which gives 7x = 147.
3. Divide both sides of the equation by 7: x = 21.

Therefore, the restaurant starts to turn a profit when it sells 21 units of its product.