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.

$\backslash$table$[[$Month$,$Jan,Feb,Mar,Apr,May,June$],[$Demand$,400,400,620,520,420,400],[$Working days,$24,23,27,24,26,26]]$

$1.$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?

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