what does x*=i/5px mean in optimization and how to interpret it? does it have the expected traits of a demand curve

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter3: Preferences And Utility
Section: Chapter Questions
Problem 3.6P
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 what does x*=i/5px mean in optimization and how to interpret it? does it have the expected traits of a demand curve 

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