Angels Inc. fabricates garage doors. Roofs are punched in a roof punching press $($R$-$Punch$)$ for $7$ minutes per roof, and then are formed in a roof forming press $($R$-$Form$)$ for $6$ minutes per roof. Bases are punched in a base punching press $($B$-$Punch$)$ for $6$ minutes per base, and then formed in a base forming press $($B$-$Form$)$ for $9$ minutes per base. The formed base is welded in a base welding machine $($Weld$)$ for $6$ minutes per base. The base and the roof then go to final assembly $($Assembly$)$ which takes $5$ minutes per garage door. There is one operator and one machine at each station. The operator and the machine work as a single server.

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$1.$ What is the Theoretical Flow Time? $($The minimum time required to produce a garage door from start to finish.$)$ The potential answers are:

A: $56$ minutes.

B: $37$ minutes.

C: $26$ minutes.

D: $43$ minutes.

E: $35$ minutes.

$2.$ What is the capacity of the factory, in terms of garage doors per hour? The potential answers are:

A: $6\mathrm{.}67$ units.

B: $3\mathrm{.}53$ units.

C: $4\mathrm{.}62$ units.

D: $3\mathrm{.}33$ units.

E: $3\mathrm{.}16$ units.

$3.$ Where is the bottleneck? The potential answers are:

A: B$-$Form

B: B$-$Punch

C: R$-$Form

D: All

E: Assembly

$4.$ Suppose we double the capacity of the bottleneck$($s$)$ by adding the same capital and human resources to each bottleneck. What is the new capacity of the system in terms of garage doors per hour? The potential answers are:

A: $3\mathrm{.}75$ units.

B: $8\mathrm{.}57$ units.

C: $4\mathrm{.}29$ units.

D: $3\mathrm{.}16$ units.

E: $4$ units.

$5.$ Where is the new bottleneck? The potential answers are:

A: Weld

B: R$-$Punch

C: B$-$Punch

D: As$-$ sembly

E: R$-$Form