All$-$Star bats sells aluminum bats to colleges. The monthly demand for bats is $1500($throughout the year$),$ and it costs $$20$ to produce a bat. The holding cost is about $$1$ per bat per year. It costs $$250$ to set up each production run.

How many bats should All Star produce in each production batch?

Assume the holding cost and price of a bat in the market are fixed. A foreman has proposed that the production cost of a bat can be reduced by $20$ cents by making a process change. However, this will increase the setup cost to $$1000.$ Should All$-$Star implement this change?