This product is assembled in an assembly plant, including $30$ workers. Each month includes $22$

working days, and the regular daily working hours are $8$ hours. Each worker is paid $$20$ per hour

in regular working times, and $$30$ per hour for overtime. The time required to assemble each unit

of product is $2\mathrm{.}2$ labor$-$hour. To satisfy the demand for the coming year, the production manager

needs an aggregate plan. Since there is a surge in demand from the seventh month $($July$),$ the

manager has decided to split the planning horizon into two periods of six months.

For the first six months, from January to July, the decision is to adjust $($hire or fire$)$ the number of

workers in a way to produce the average demand over this period internally and, for those periods

where the internal production is not sufficient to cover demand, the quantity needed will be

outsourced with a price of $$30$ per unit.

For the second six months, from July to the end of December, the decision is to adjust $($hire or fire$)$

the number of workers in a way to produce the average demand over this period internally and, if

there is a period where the internal production is not sufficient, the quantity needed will be done in

overtime.

There is no inventory in the beginning, and no inventory must be left at the end of the planning

horizon.

Unit inventory holding cost is $$0\mathrm{.}5$ per month. Also, hiring and firing costs are $$500$ and $$1000$ per

worker, respectively.

Develop the aggregate plan and calculate the total cost of the plan