Oasis Pty$.$ Ltd$.$ just got a new contract to produce $280$ units per week of each of three items A$,$B and C$.$ Oasis has five machining centres $($milling$,$ turning, bending, drawing and painting centres$).$ The batch set$-$uptime $($in hours$)$ and unit processing time $($in minutes$)$ for each of the new items to be produced at each of the centres is given in Table $1.$ The current utilisation of the work centres before the new contract was secured is shown in Table $2.$This utilisation is calculated based on the effective $($available$)$capacity and not the design$($installed$)$ capacity. Each machine centre works $24$ hours a day, $6$ days a week. Assembly is done manually. Each worker works $8$ hours each day. Assembly workers work $5$ days a week. The unit assembly time $($in minutes$)$ for each of the items is also given on Table$1.$ Labour efficiency is $0\mathrm{.}85.$ Oasis has to hire new assembly workers for the new order they just got. Labour is very scalable and hence, is hardly considered as a constraint. If Oasis runs short of capacity, they will choose to continue producing all the old orders and seek to maximise the total number of items$($A$,$ B and C$)$ produced from the new order because they make the same profit from every unit of A$,$B or C produced and any unit of A$,$ B or C not produced in house can be subcontracted to vendors if necessary. Based on principles of the Theory of Constraints: $($a$)$Determine the design and effective capacities for the machines.

$($b$)$ Using the pre$-$contract utilisation, determine the load that exists on each machine centre before the new contract was secured. $($c$)$ Determine the load from the new order and the total load on the work centres, including the load from the new order. d$)$ Identify the most critical machining centre. e$)$ Given management policy when constrained by capacity, which of the items would be subcontracted and what quantity would it be$?$ f$)$ How many new assembly workers would Oasis need to hire, given that the workers cannot be cross$-$trained?

Table $1$: Set Up and Processing Times for Products A$,$ B$,$ and C

Table $2$: Existing Load on Work Centers