The Pullman$$ Mfg$.,$ Inc.,$$ three$-$station work cell illustrated in the figure below has two machines at station $1$ in parallel.$($The product needs to go through only one of the two machines before proceeding to station$2.)$

Station $1$

Station $1$

Station $2$

Station $3$

$20$ min$/$unit

$20$ min$/$unit

$3$ min$/$unit

$12$ min$/$unit

A figure has four rectangles. The first two are parallel and arranged vertically, with the first being on top and the second being on the bottom. The first rectangle is labelled "Station $1,$ Machine A$,20$ minutes per unit". The second rectangle is labelled "Station $1,$ Machine B$,20$ minutes per unit". An arrow points from these two rectangles to the third rectangle. The third rectangle is labelled "Station $2,3$ minutes per unit". An arrow points from the third rectangle to the fourth rectangle. The fourth rectangle is labelled "Station $3,12$ minutes per unit".

The$$ manager, Ms$.$ Hartley, has asked you to evaluate the system if she adds a parallel machine at station $.$

Part $2$

$$a$)$ The throughput timeLOADING... of the new work cell is

$$

$35$ minutes. $($Enter your response as a whole$$ number.$)$

Part $3$

$$b$)$ The bottleneck timeLOADING... of the new work cell is

$$

$10$ minutes per unit. $($Enter your response as a whole$$ number.$)$

Part $4$

$$c$)$ If the firm operates hours per$$ day, $6$ days per$$ week, the weekly capacityLOADING... of the work cell with the second machine at workstation is

$$

$432$ units.$($Enter your response as a whole$$ number.$)$

Part $5$

$$d$)$ If the firm operates hours per$$ day, $6$ days per$$ week, the weekly capacity of the work cell without the second machine at workstation is units. The second machine at workstation moves the bottleneck to workstation

$$

$1,$ with a process time of

$$

$10$ minutes per$$ unit, which increases the capacity by

$$

$2$ units per week. $($Enter your responses as whole$$ numbers.$)$