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Parts $P1 – P7$ are machined first on a milling machine and then polished at a separate machine. Using the information in the following table, the minimum total completion time required tor carrying out both the operations for all $7$ parts is _____________ hours.

$$\begin{array}{|c|c|} \hline
\text{Part} & \text{Milling (hours)} & \text{Polishing (hours)} \\ \hline\text{P 1} & 8  & 6 \\ \hline \text{P 2} & 3  & 2 \\ \hline\text{P 3} & 3  & 4 \\ \hline \text{P 4} & 4  & 6 \\ \hline \text{P 5} & 5  & 7 \\ \hline \text{P 6} & 6 & 4 \\ \hline \text{P 7} & 2  & 1 \\ \hline \end{array}$$

  1. $31$
  2. $33$
  3. $30$
  4. $32$
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