The learning curve phenomenon is one of the reasons why an assembly line with n stations is capable of out$-$producing n single workstations, where each single station does the entire work content of the job. Consider the case of a product whose theoretical work content time for the first unit is $20$ min. The effect of an $85$ percent learning rate is to be compared for two cases, using the Crawford learning curve model: $($i$)10$ single workstations, each doing the entire assembly task, and $($ii$)$ one perfectly balanced $10$ station assembly line, where each station does $2\mathrm{.}0$ minutes of the total work content.

Using the Crawford learning curve model, determine the production rate for the $1000$th unit produced for:

$($a$)$ The $10$ single workstations.

Production rate for $10$ single workstations in units per hour Rp $=$ Answer

$($b$)$ The $10$ station assembly line assuming perfect balance.

Production rate for the line in units per hour Rp $=$