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A student has two sources of expenses: living and consumption. if the student lives in an apartment with s square meters and consumes c consumables

A student has two sources of expenses: living and consumption. if the student lives in an apartment with s square meters and consumes c consumables then they receive utility

u (s, c) = s1/5 c4/5

The student chooses apartment size and consumption amount to get the highest utility. Total l living expenses are 1000+rs. Each unit of consumption costs 1. The students spends exactly 1800.

Building restrictions require apartments to be at least 20 square meters but no more than 120 square meters.

a. List all the cases that will occur from complementary slackness, with the implied equations and checks for each case.

b. Under what conditions will the student live in a 20 m ^2 apartment? a 120M^2 apartment ? an apartment between 20 m^2 and 120 m^2?

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