Consider the Part Type Selection problem we covered in class. This problem helps us determine which parts we will

produce in a new FMS$.$ The problem assumes that we have candidate parts $i=1,2,$dotsN, that the total savings achieved

by producing part $i$ in the FMS is $s_i$ and that we know that there is a 'key bottleneck' in the FMS$,$ which has $P$ available

time units. Each part i requires a total processing time $p_i$ in the 'key bottleneck'.

$,$ Step $1$: Order parts $[1]$ to $[$N$]$ such that

$-\frac{s_{[1]}}{p_{[1]}}\frac{s_{[2]}}{p_{[2]}}$cdots$\frac{s_{[N]}}{p_{[N]}}$

$,$ Define remaining available time $T=P$

Step $2$: For $i=1$dotsN select part i and add the part to the FMS if $s_i>0iT=T-p_{i}P,QRi{p}_i,q_i{r}_i{p}_i$ and $s_i>0.$ Each time you add a new

part $i,$ update the remaining available time $asT=T-p_i.$

Now suppose you had $3$ 'key bottlenecks' $(thatis3$ resources that each might $be$ the bottleneck depending $on$ the

parts you choose $to$ produce $in$ the $FMS).$ These resources have $P,Q$ and $R$ time units available respectively. And

each part i requires a total processing time $p_i,q_i$ and $r_{i}in$ each $of$ the three, respectively. Modify the algorithm

above $to$ solve the $3-$bottleneck version $of$ the problem