a$.$ Develop an aggregate production plan for four months with the following details:

Material cost $=$ Rs $100$ per unit

Inventory holding cost $=$ Rs $10/$unit$/$month

Marginal cost of stock out $=$ Rs $20/$unit$/$month

Marginal cost of subcontracting $=$ Rs $200$ per unit

Hiring and training cost $=$ Rs $50$ per worker

Layoff cost$=$ Rs $100$ per worker

Labour hours required$=4$ man$-$hrs per unit

Regular pay$($ eight hours per day$)=$ Rs $12$ per hour

Overtime pay$=$ Rs $20\mathrm{.}00$ per hour.

Beginning inventory $=100$ units

$***$No Safety stock required. Normal working hours $8$ per working day

Demand and working days for each month

$\backslash$table$[[,$Jan,Feb,Mar,Apr$],[$Demand$,500,600,450,700],[$Working Days,$22,19,23,21]]$