Final answer:
The question covers probability theory to determine revenue distribution and microeconomics for calculating profit-maximizing quantities for a firm. Students must use graphing and mathematical calculations to solve problems in both contexts.
Step-by-step explanation:
The student asks a question related to probability and revenue calculation for a vendor selling pens at different price points and relating it to concepts such as the exponential distribution and profit maximization for a company selling products. Specifically, it involves finding the probability that a random variable falls within a certain interval and calculating total revenue, marginal revenue, total cost, and marginal cost for a firm in a perfectly competitive market to determine the profit maximizing quantity.
To address the question, one would need to apply concepts from probability theory and basic microeconomic principles of firm production and market behavior. The student is expected to graph the situation and utilize calculations to inform decision-making within the context given.
- For probability-related questions, it would be necessary to use the properties of the exponential distribution to find the probability within a certain range.
- In the economics context, the student would calculate the total revenue by multiplying the number of units sold by the price per unit. Marginal revenue is the additional revenue from selling one more unit, while total cost is the sum of fixed and variable costs. Marginal cost is the additional cost incurred from producing one more unit. Graphs of these values could be used to visually assess the profit maximizing output.