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:

PRODUCTION MONTH

$1234$

PRODUCTION COST PER AIR CONDITIONER

$$500$ $$550$ $$520$ $$500$

PRODUCTION CAPACITY

$650650750800$

ESTIMATED DEMANDS

$600700900550$ HOLDING

COST PER AIR CONDITIONER

$$10$ $$12$ $$15$ $$12$

a$.$ Formulate an LP model for this problem. b$.$ Construct an Excel Spreadsheet and use Solver to solve this problem. What is the optimal production and inventory plan?

MONTH $1$

PRODUCTION 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?

MONTH