$(25$ points$)$ A restaurant chain is hiring temporary workers at two locations to help with their burgeoning business. Three temporary workers are available. Worker A has $20$ hours$/$week available, and charges $$10/$hour and $$15/$hour for Location $1$ and $2$ respectively. Worker B has $15$ hours$/$week available, and charges $$12/$hour and $$10/$hour for Location $1$ and $2$ respectively. Worker C has $18$ hours$/$week available, and charges $$14/$hour and $$12/$hour for Location $1$ and $2$ respectively. Location $1$ and $2$ each need $30$ hours$/$week$.$ The restaurant seeks to find the least expensive way to hire temporary workers. Answer the following questions: a$)(10$ points$)$ Draw the network representation of this problem. b$)(15$ points$)$ Formulate an LP problem. $($Hint: Check the relationship between the total supply and total demand.$)$