Each week a U$.$S$.$ consumer may prepare home cooked meals $(1$q $)$ as well as eat out at a

restaurant $(2$q $).$ Suppose the average price of a home cooked meal $$25,$ the price of eating out

is $2=50,$ and average spending is $$500$ per week. The typical consumer picks $1$q and $2$q to

maximize utility function $=1$

$0\mathrm{.}752$

$0\mathrm{.}25$ subject to their budget.

$1.$ Based on the Lagrangian problem reviewed in the video lecture $($and in the book$),$ write out

the general consumer demand functions that we found for $1$q and $2$q $,$ and then calculate

what these are for the situation described above. How many meals are eaten at home

versus out per week?