Question

Suppose that the total cost function, in dollars, for the production of x units of a product is given by the equation shown below:

C(x) = 9,680 + 60x + 0.2x²

The average cost of producing x units is given by:

(C(x) / x) = (9,680 + 60x + 0.2x²) / x

Answer 1

a. The average cost of producing x units, denoted as Cₓ, is given by Cₓ = 9680/x + 60 + 0.2x.

Step-by-step explanation:

a. The average cost of producing x units is found by dividing the total cost function C(x) by the number of units x. In this case, the total cost function is given as C(x) = 9680 + 60x + 0.2x², and the average cost is expressed as Cₓ = C(x) / x. To simplify this expression, divide each term in C(x) by x, resulting in Cₓ = 9680/x + 60 + 0.2x.

Understanding average cost is essential in economics and business management. It represents the cost per unit of production, providing insight into the efficiency of the production process. In this context, the average cost formula Cₓ allows for the calculation of the average cost for producing each additional unit, taking into account fixed and variable costs.

In summary, the average cost function Cₓ = 9680/x + 60 + 0.2x is derived from the given total cost function C(x) by dividing each term by x. This expression provides a concise representation of the average cost per unit for producing x units of a product, incorporating fixed and variable costs.