Millennium Electronics produces two air conditioner models, Model A and Model TL$.$

The demand for air conditioners for these two models for the next $6$ months is provided in the following table.

$\backslash$table$[[$Month$,1,2,3,4,5,6],[$Demand $($air conditions$),40,85,70,80,75,90]]$

Currently, the company has $10$ workers, and each worker produces $5$ air conditions per month. The operations manager is about to prepare an aggregate production plan that covers the next six months. The opening inventory is $10$ air conditions. The cost and production information is as follows.

Cost Data

Regular$-$time labour cost

Overtime labour cost

Subcontracting cost

$$20$ per air condition

$$30$ per air condition

$$60$ per air condition

Holding cost

Hiring cost

Firing cost

$$10$ per air condition per month

$$100$ per worker

$$50$ per worker

Production: Maximum overtime output is $15$ air conditioners per month

The manager would like to make an aggregate planning by keeping initial workforce level for next $6$ months, and using overtime and subcontract as needed. The manager also would like to use initial inventory as early as possible, ensure no shortages for any month, and keep $20$ air conditions in inventory in the end of month $6$ in this plan. Please use the table in the "Data & Tables file$-$Term Test II$"$ file $($sheet Q$1(1))$ on Brightspace to develop an aggregate plan. What is the total coct of thic icmt