As a manager, you must decide $($on the basis of annualized costs$)$ which type of machine and how many to buy given two altemative technologies: A and B $.$

Technology related information:

Demand Information:

Product forecasts and processing times on each type are as follows:

Operations related information:

The products need to be produced in batches due to positive setup times. The relevant information is given below.

The firm plans to have one shift per day. The shift works for $8$ hours per day for $300$ days in a year. In addition to the information given above, suppose all of the following also hold:

$($i$)$ The management desires to employ a capacity cushion of $\backslash (10\backslash \%\backslash ).$

$($ii$)$ Every operating hour incurs a cost of $\backslash (\backslash$$ $10\backslash )$ on machine type A and $\backslash (\backslash$$ $13\backslash )$ on machine type $\backslash ($ B $\backslash ).$

$($iii$)$ Each machine of either type requires one worker as an operator. The wage of worker is $\backslash (\backslash$$ $11\backslash )$ per hour on a machine of type $\backslash ($ A $\backslash )$ and it is $\backslash (\backslash$$ $12\backslash )$ per hour on a machine of type B$.$ The firm computes the operators' labor cost on the basis of actual operational time,

$($iv$)$ The firm charges an overhead calculated at $\backslash (25\backslash \%\backslash )$ of direct labor costs.

$($v$)$ For all products, type $\backslash ($ A $\backslash )$ has $6-$sigma quality. Type $\backslash ($ B $\backslash )$ has a process capability ratio $\backslash ($ C$\_\{$p$\}\backslash )$ of $1\mathrm{.}4$ for product $1$ and a $\backslash ($ C$\_\{$p$\}\backslash )$ of $1\mathrm{.}50$ for product $2.$ Each unit of Product $1$ produced at the design tolerance limits incurs a cost of $\backslash (\backslash$$ $5\backslash )$; this cost is $\backslash (\backslash$$ $4\backslash )$ for Product $2.$

The firm management desires to investigate the impact of process capability on the production system decision. $($Hence$,$ they evaluate total costs with $($a$)$ costing only defective proportion of output and $($b$)$ costing all production considering all imperfections.$)$