Final answer:
The cost of producing x units is calculated using the function C(x) = 800 + 80x - 80 ln(x), which includes fixed costs, variable costs, and economies of scale. To find the cost for a specific number of units, substitute that number into the equation for x.
Step-by-step explanation:
The cost of producing x units of a product is given by the cost function C(x) = 800 + 80x - 80 ln(x), where x ≥ 1. In this function, 800 represents the fixed costs, which are present regardless of the level of production. The term 80x corresponds to the variable costs, which are proportional to the number of units being produced. The term -80 ln(x) reflects the savings associated with economies of scale, where producing more units can reduce the cost per unit. To determine the cost of producing a certain number of units, you would substitute that number into the function for x and calculate the total cost.
As an example, if we want to calculate the cost of producing 10 units, we would compute C(10) = 800 + 80(10) - 80 ln(10). The result would give us a specific value representing the total cost of production for 10 units.