Problem $4$: $(20$ points$)$

To develop an aggregate plan for January$-$June, a production manager has collected the following data

Cost: $($AED$)$

Inventory holding $10/$unit$/$month

Regular time $,100/$hour

Subcontract $,50/$unit

Hiring $500/$worker

Firing $700/$worker

$\backslash$table$[[$Month$,$Jan,Feb,Mar,Apr,May,June,Total$],[$Demand$,500,400,550,600,500,550,3100]]$

Other data

Current workforce $10$ workers

Labor hour$/$unit $4$ hours

Working days$/$month $25$ days

Working hours$/$day $8$ hours

Evaluate the following strategies

a$-$ Vary the workforce to meet exactly the demand

$\backslash$table$[[$Month$,$Jan,Feb,Mar,Apr,May,June,Total$],[$Demand$,500,400,550,600,500,550,3100],[$# workers,,,,,,,$],[$Production$,,,,,,,],[$Hiring$,,,,,,,],[$Firing$,,,,,,,]]$

b$-$ Produce at constant rate of $500$ units$/$month$.$ Use subcontract when needed

$\backslash$table$[[$Month$,$Jan,Feb,Mar,Apr,May,June,Total$],[$Demand$,500,400,550,600,500,550,3100],[$Production$,,,,,,,],[$Inventory$,,,,,,,],[$Subcontract$,,,,,,,]]$