Please help i need to find an equation for word problem

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SUMMARY

The discussion focuses on formulating an equation to maximize airline ticket revenue based on pricing strategies. The airline sells 300 additional tickets per day at a $200 price point, with a $10 reduction leading to 30 more tickets sold. The correct approach involves defining the revenue function in terms of ticket price and quantity sold, ultimately leading to a quadratic equation that can be solved using calculus techniques. The user successfully identifies the dependent variable as revenue, paving the way for further calculations.

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  • Understanding of revenue maximization concepts
  • Familiarity with quadratic equations
  • Basic calculus principles, particularly differentiation
  • Ability to manipulate equations into the y= form
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  • Learn how to derive revenue functions from pricing models
  • Study quadratic functions and their properties
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  • Practice setting up equations from word problems
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Students in mathematics or economics, particularly those tackling optimization problems in calculus, as well as educators looking for examples of real-world applications of quadratic equations.

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Homework Statement



An airline finds that if it prices a ticket at $200, it will sell 300 more tickets per day. It estimates that each $10 price reduction will result in 30 more tickets sold per day. Find the ticket price and number of tickets sold that will maximize the airline's revenue. Use calculus to solve.

Homework Equations



This is what I need help with; I know how to find the maximum and minimum of an equation, but I can't figure out how to make an equation for this problem. It needs to be in y= form for me to solve but I'm struggling to figure it out.

The Attempt at a Solution


I came up with $200-10x=300+30x
but I can't work with that since it's not in y= and I don't think I set the variables up right anyways. Please help! I can't find the max revenue until I find the actual equation! Thanks
 
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The first step is to reread the question part of the problem statement: "Find the ticket price and number of tickets sold that will maximize the airline's REVENUE." This part gives you a strong indication as to what your dependent (y) variable should be.
 
Okay, I'm just now figuring out this site, but I figured it out so thanks!
 

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