Consider a single machine that can do operations on $3$ part types. The operation time for part i is $\backslash$tau i$,$ i $=1,2,3.$ The set$-$up time from part i to part j $!=$ i is S$,$ independent of i and j$.$

Assume that the machine is perfectly reliable and operated as follows:

$$ The lot size of type i parts is Qi$.$

$$ Parts are produced in the following sequence: $1,2,3,1,2,3,...$ That is$,$ a lot of type $1$ is worked on$,$ followed by a set$-$up change from $1$ to $2,$ followed by work on a type $2$ lot, followed by a set$-$up change from $2$ to $3,$ followed by work on a type $3$ lot, followed by a set$-$up change from $3$ to $1,$ etc. $($This is called a round$-$robin sequence.$)$ In this example, a set$-$up cycle is a period in which $1$ batch of each part type is produced, and in which there are $3$ set$-$ups. $$

$$ The machine is never allowed to be idle.

Part $1$

How much time is required from the completion of a type i lot to the completion of a type $j$ lot where $j=i+1$ if $i$

$=1$ or $2$ ; and $j=1$ if $i=3?($Enter $Tj$ for ${}_j$ and $Qj$ for $Q_j)$

$($Please enter expression$)$

You have used $0$ of $3$ attempts

Part $2$

What is the duration of a set$-$up cycle? $($Enter Q$1,$Q$2,$Q$3$ for $Q_i$ and T$1,$T$2,$T$3$ for ${}_i)$

Part $3$

Find $C$ for $1=1,2=2,3=3,Q1=10,Q2=8,Q3=6,S=2.$

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