2 Problem 2: Dynamic Pricing Background: You are a pricing analyst for a popular concert venue. The venue has a capacity of 5,000 people. The concert tickets are initially priced at $50 each, and you are considering implementing dynamic pricing to maximize revenue. Based on historical data and market research, you know that your customer base can be segmented into three groups: 1. "Early Birds": These customers purchase their tickets as soon as they go on sale. They are price-sensitive. The segment makes up about 40% of the total customer base. The price-demand function for this group is given by D = 3000 - 20(P - 50), where D is the demand and P is the price. 2. "Regulars": These customers purchase their tickets about a month before the concert. They are moderately price-sensitive. The segment makes up about 35% of the total customer base. The price-demand function for this group is given by D = 2500 - 15(P - 50). 3. "Last Minute": These customers purchase their tickets in the week before the concert. They are the least price-sensitive and are willing to pay a premium for last-minute tickets. The segment makes up about 25% of the total customer base. The price- demand function for this group is given by D = 2000 - 10(P - 50). Problem: Your goal is to maximize the venue's revenue by implementing a dynamic pricing strategy. However, you must also ensure that you do not exceed the total venue capacity of 5,000 seats. 1. Given the above segmentation and the price-demand functions, calculate the optimal price for each segment that maximizes revenue for the venue without exceeding the total capacity. 2. Provide a justification for your proposed prices, and discuss how they match the price sensitivity of each segment. 3. What is the maximum revenue that the venue can expect if your pricing strategy is implemented successfully, keeping in mind the capacity constraints? 4. Discuss potential risks of your proposed strategy and how you would mitigate them.]