For the following monthly demand forecast develop an aggregate plan when

a$)55$ units per day is produced and unmet demand is backordered.

b$)42$ units per day is produced and overtime is used when needed.

$\backslash$table$[[\backslash$table$[[$Mont$],[$h$]],\backslash$table$[[$Deman$],[$d$]],\backslash$table$[[$Production$],[$Days$]]],[1,1175,20],[2,1600,22],[3,1300,21],[4,900,21],[5,900,19],[6,1000,22]]$

$\backslash$table$[[$item$,$cost$],[$Inventory carrying cost,$$5$ per unit per month$],[$Subcontracting cost per unit,$$20$ per unit$],[$Average pay rate, per day$)]]$

$\backslash$table$[[$Overtime pay rate,$\backslash$table$[[$$$\frac{17}{h}r,($above$],[$hrs$/$day$)]]],[$Labour$-$hours to produce a unit,$1\mathrm{.}6$ hours per unit$],[\backslash$table$[[$Cost of increasing daily production rate $($hiring and$],[$training$)]],$$$300$ per unit$],[$Cost of decreasing daily production rate $($layoffs$),$$$600$ per unit$],[$Backorder$,$$$10$ per unit$]]$