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$

$\backslash$table$[[,$MONTH $1,$MONTH $2,$MONTH $3,$MONTH $4],[$PRODUCTION$,,,,],[\backslash$table$[[$ENDING$],[$INVENTORY$]],,,,]]$

c$.$ What is the total cost of this plan?

d$.$ Using the sensitivity report, if the company is able to rent extra storage room, which month should it do so$?$ What is the most the company should pay per unit in this period?

Create the Sensitivity Report and use it to answer the following question:

d$.$ Using the Sensitivity Report, if the company can increase production capacity, which month$($s$)$ should it do so$?$ What is the most the company should pay per unit in this period $($assuming only one change is allowed at a time$)?$