$.(15$ pts$).$ Suppose that Plant $2$ must shut down and is no longer able to contribute to making Products $1$ and $2.$

However, Plant $1$ is able to provide more hours. $($None of the other assumptions associated with original

example change. Plant $3$ still limited to no more than $18$ hours available. $)$

You need to answer: how many additional hours does Plant $1$ need to work to maximize the profit under these

conditions and what is the new profit value? $($Denote the additional hours for Plant $1$ as variable $$y$.)$

a$.(5$ pts$)$ Identify the feasible region and how it changes from original problem.

b$.(5$ pts$).$ Write down the modified LP problem formulation.

c$.(5$ pts$)$ Find the value of $$y$,$ and identify new optimal solution, and new value of objective function Z$?$