Final answer:
The profit function for Kaylee's business selling n hiking bags is represented as Profit(n) = p × n - (vc × n + fc), where p is the price per bag, vc is the variable cost per bag, and fc is the fixed cost. Examples provided include a situation where at the output level of 5 bags, there can be either lost or zero profit based on the cost and price settings.
Step-by-step explanation:
Kaylee's profit from selling n hiking bags is the difference between her total revenue and her total expenses. The function to represent this would be Profit(n) = Total Revenue - Total Expenses. Let's assume that the price per hiking bag is p, and her total cost of producing n bags is a combination of variable costs vc and fixed costs fc. Therefore, the total revenue would be p × n, and total expenses would be vc × n + fc. The profit function becomes Profit(n) = p × n - (vc × n + fc). This equation will allow Kaylee to calculate her profits based on the number of bags sold.
Using an example, if Kaylee determines her profit-maximizing output level is 5 bags, and her profit at that level is $40, we can relate it to another scenario. If p is $25 per unit and the total cost for producing five units is $130, then her total revenue is $125 (5 × $25) and she experiences losses of $5 at this output, which denotes negative profits. In contrast, if the firm sells 75 packs at $2.75 each without incurring profit or loss, it implies zero profit, as total revenue and total cost are equal, both being (75) × ($2.75).