$1\mathrm{.}3.$ Question $3.$

Mixed stratesy $($allowing inventory and workforce changes from month to month$)$: Fi$.$ an notimal plan $($using linear programming$)$ to meet all monthly demands $($assumi$.$ back order not allowed$)$ in order to minimize the total cost including employee hiring and firing costs and inventory carrying cost.

Defining Variables:

$C_H=$ Cost of hiring.

$C_F=$ Cost of firing.

$C_{\text{I}}=$ Cost of inventory.

$P_i=$ Production during month $\text{'}i\text{'}.$

$W_i=$ Number of workers during month $\text{'}i\text{'}.$

$W_O=$ Workers employed at the beginning.

$I_O=$ Inventory at the beginning.

$I_i=$ Inventory during month $\text{'}i\text{'}.$

$D_i=$ Demand during month $\text{'}i\text{'}.$

$d_i=$ Number of working days during month $\text{'}i\text{'}.$

$H_i$ and $F_i=$ Number of workers hired and fired during month $\text{'}i\text{'}.$

For all $i=1,2,3.$