Consider you have two plants$($in Philadelphia and$$ Pittsburgh$)$ and two destination sites$($markets$),$ in Baltimore and New York. You are considering expansion and would like to add a third plant in either Buffalo or Cleveland. The per unit transportation costs are given on each$$ route as follows.

Baltimore New York Capacity

Philadelphia $10011020$

Pittsburgh $40047525$

Buffalo $60055020$

Cleveland $40047520$

Demand $4025$

The expected supply in both Buffalo and Cleveland is $20$ units.

$$Set up and solve two transportation problems whose solutions will help you select the new location:

$($a$)$ What costs do you get with$$ Buffalo?

$[$ Select $]$

$($b$.)$ What costs do you get with$$ Cleveland?

$[$ Select $]$

$($c$.)$ What location would you be your$$ decision?

$[$ Select $]$

$($d$.)$ Consider when Cleveland is included, if you were forced to send two units from Philadelphia to$$ Baltimore, what will be the new$$ cost$?$

$[$ Select $]$