How do I model the optimization of haircuts (price vs. frequency vs. satisfaction)?

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My goal is to use a simple, real world situation to apply optimization algorithms to and find optimal choices based on computation. What information do I need to gather and what questions do I need to ask? In the end, I want to be able to say that yearly pattern $x$ of haircuts is the most optimal based on price, frequency, and satisfaction. How do I begin to define the variables of this problem? How would I even model satisfaction level??

Example inputs:

hair growth rate = 1 inch/month

satisfaction =

a. 3 inches = 10/10 (perfect satisfaction)

b. 3.5 inches = 9/10

c. 4 inches = 8/10

d. 5 inches = 5.5/10 (sharp decline)

e. 6 inches = 4.5/10

price of haircut = $20 (ludicrous, I know)