Final answer:
The domain of the cost function c(x) = 200 + 16x represents the set of all non-negative whole numbers, which are the possible quantities of complete products a factory can manufacture. This ties into the production function and the calculation of total costs, combining fixed and variable expenses.
Step-by-step explanation:
The domain of the production cost function c(x) = 200 + 16x represents all the possible number of complete products manufactured in the factory. This relates to the firm's production function, which helps to determine the total cost by identifying the number of inputs needed to produce a given quantity of output. The fixed costs are included as $200, regardless of the production level, and variable costs are accounted for by the 16x, where 'x' is the quantity of products produced.
In this context, the domain would consist of all non-negative integers since you cannot manufacture a negative amount of products and manufacturing typically results in whole products. Therefore, the domain in realistic terms is the set of all non-negative whole numbers, reflecting the possible scenarios of production from zero to the maximum capacity of the factory.