Deciding on Capacity

You are a division manager for Wayne Biotech, and are tasked with deciding on the capacity of your new factory for a new ecologically friendly weed killer. A similar new product has been developed by Isley Industries. The demand for the new weed killer is given $=482,$ where $$ is the price, $=!+!,$ and $!$ and $!$ are the quantity produced by Wayne and Isley, respectively. Wayne$$s cost of production per unit is $4$; Isley$$s cost of production per unit is $2.$

a$)$ Wayne and Isley will simultaneously decide on the capacity of their production facility, i$.$e$.,$ each will simultaneously decide on quantity. What quantity will you produce? What quantity do you expect Isley to produce? What are your expected profits?