a$)$ What is the optimal aggregate plan for a wine distributor company that imports and

repackages wine for retail sale? The company has $20$ employees, each capable of packaging $1000$

bottles of wine per day. The inventory holding cost is $$1$ per bottle per month, and the backlog

cost is $$2$ per bottle per month. The workers earn $$2000$ each per month. Given the demand and

working days for January to June, assess the aggregate plan without allowing backlogs, and

determine if cost savings can be achieved by permitting backlogs.

$1.$b$)$ The distributor company is contemplating the utilization of temporary personnel during peak

demand periods. These temporary workers can be sourced from a local staffing agency, incurring

a cost of $$2800$ per month along with a one$-$time fee of $$1000.$ If the temporary workers exhibit

efficiency comparable to regular employees, is it possible for the company to lower its expenses

by hiring temporary staff?