The operation manager of EasyCool Co$.,$ a manufacturer of air conditioners, is now scheduling the production plan for the next four months. They will incur an inventory cost for each unsold air conditioner at the end of every month. The company now has $150$ air conditioners available and is required to hold at least $80$ air conditioners at the end of month $4.$ Information for the next four months is given as follows:

$\backslash$table$[[\backslash$table$[[$PRODUCTION$],[$MONTH$]],\backslash$table$[[$PRODUCTION$],[$COST PER AIR$],[$CONDITIONER$]],\backslash$table$[[$PRODUCTION$],[$CAPACITY$]],\backslash$table$[[$ESTIMATED$],[$DEMANDS$]],\backslash$table$[[$HOLDING$],[$COST PER AIR$],[$CONDITIONER$]]],[1,$$$500,650,600,$$$10$