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? $(20$ points$)$

b$)$ You have the ability to accelerate the building of your production facility, but doing so will

increase the total cost $($not the cost of producing each unit$)$ of the facility by $7.$ If you do so$,$

Isley will observe your capacity before choosing the capacity of their plant. What quantity

will you choose if you accelerate the building of your plant? Is accelerating the building of

your production facility worthwhile? Why or why not? $(20$ points$)$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? $(20$ points$)$

b$)$ You have the ability to accelerate the building of your production facility, but doing so will

increase the total cost $($not the cost of producing each unit$)$ of the facility by $7.$ If you do so$,$

Isley will observe your capacity before choosing the capacity of their plant. What quantity

will you choose if you accelerate the building of your plant? Is accelerating the building of

your production facility worthwhile? Why or why not? $(20$ points$)$