**Cruise Line Ticket Pricing and Profit Maximization**A cruise line sells tickets to two kinds of passengers: luxury and economy class. Economy passengers pay $400 per ticket, while luxury passengers pay $800. The cost (in hundreds of dollars) of taking $ x $ economy passengers and $ y $ luxury passengers is thought to be:\[C(x, y) = 3x + 5y + \frac{x^2}{400} + \frac{2xy}{200} + \frac{2y^2}{100} + 35\]**Objective:**Determine the number of tickets to sell in each class to achieve maximum profit.**Tasks:**- **Economy Passengers:** How many economy passengers would lead to the highest profit? - **Luxury Passengers:** How many luxury passengers would lead to the highest profit?**Your Job:** Use the cost function to figure out the optimal number of passengers for each ticket category to achieve maximum profit.

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A cruise line sells tickets to two kinds of passengers, luxury and economy class. Suppose that economy passengers pay $ 400 per ticket, while luxury passengers pay $ 800. The cost (in hundreds of dollars) of taking a economy passengers and y luxury passengers is though to be 2y² x² 2xy + 400 200 100 C(x, y) = 3x + 5y + + +35 Your job is to find out how many tickets of each type would lead to the maximum profit. How many ecomony passengers would lead to the highest profit? How many luxury passengers would lead to the highest profit?

A cruise line sells tickets to two kinds of passengers, luxury and economy class. Suppose that economy passengers pay $ 400 per ticket, while luxury passengers pay $ 800. The cost (in hundreds of dollars) of taking a economy passengers and y luxury passengers is though to be 2y² x² 2xy + 400 200 100 C(x, y) = 3x + 5y + + +35 Your job is to find out how many tickets of each type would lead to the maximum profit. How many ecomony passengers would lead to the highest profit? How many luxury passengers would lead to the highest profit?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

**Cruise Line Ticket Pricing and Profit Maximization**

A cruise line sells tickets to two kinds of passengers: luxury and economy class. Economy passengers pay $400 per ticket, while luxury passengers pay $800. The cost (in hundreds of dollars) of taking $ x $ economy passengers and $ y $ luxury passengers is thought to be:

\[
C(x, y) = 3x + 5y + \frac{x^2}{400} + \frac{2xy}{200} + \frac{2y^2}{100} + 35
\]

**Objective:**
Determine the number of tickets to sell in each class to achieve maximum profit.

**Tasks:**
- **Economy Passengers:** How many economy passengers would lead to the highest profit?
- **Luxury Passengers:** How many luxury passengers would lead to the highest profit?

**Your Job:** Use the cost function to figure out the optimal number of passengers for each ticket category to achieve maximum profit.

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