Lagrangian Example Problem

Suppose a consumer's preferences are described by the utility function:


The consumer has an income $Y=100$. The price of shelter is 1 ($p_s=1$) and the price of food is 10 ($p_f=10$). Use the lagrangian method to find the consumer's demand for food and shelter, if her goal is to maximize utility subject to her budget constraint.

Try on your own before watching the following video.

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