reproducing this LP model in excel file, and use solver to find the min z

Case: AGGREGATE PLANNING

Definition

In these models, the workforce level is allowed to change each period through the hiring and firing of

workers. Such models, where we determine workforce levels and production schedules for a

multiperiod time horizon, are called aggregate planning models.

Case

Renova company is a manufacturer of fancy bags in Melbourne. The demand for the next four

months is forecasted as below:

$500$ bags are on hand at the beginning of month $1,$ and the company has $20$ workers. The wage of a

worker is $$1500$ per month. The standard working time for a worker is up to $160$ hours per month before

he or she receives overtime. The maximum overtime for a worker is $20$ hours per month and is paid

$$13$ per hour for overtime labour. It takes four hours of labour and $$15$ of raw material to make a bag.

At the beginning of each month, workers can be hired or fired. Each hired worker costs $$1600,$ and

each fired worker costs $$2000.$ At the end of each month, a holding cost of $$3$ per bag left in inventory

is incurred. Production in a given month can be used to meet that month's demand. Renova wants to

use LP to determine its optimal production schedule and labour policy.

Additional Info:

The data on the current number of workers, the regular hours per worker per month, the

regular hourly wage rates, and the overtime hourly rate, should be well known. The maximum

number of overtime hours per worker per month is probably the result of a policy decision by

management or a clause in the workers' contracts.

The costs for hiring and firing a worker are not trivial. The hiring cost includes training costs

and the cost of decreased productivity due to the fact that a new worker must learn the job.

The firing cost includes severance costs and costs due to loss of morale. Neither the hiring nor

the firing cost would be simple to estimate accurately, but the human resources department

should be able to estimate their values.

The unit production cost is a combination of two inputs: the raw material cost per bag and the