Figure $1$: A Simple Process with a Constraint

$1.$ This is a classic example used to illustrate the idea of TOC. $($Six Sigma and Beyond $-$ Thomas Pyzdek$)$

a$.$ Identify the system constraint.

b$.$ This fictitious company produces only two products, P and Q $.$ The market demand for $\backslash ($ P $\backslash )$ is $100$ units per week, and $\backslash ($ P $\backslash )$ sells for $\backslash (\backslash$$ $90\backslash )$ per unit. The market demand for $\backslash ($ Q $\backslash )$ is $50$ units per week, and $\backslash ($ Q $\backslash )$ sells for $\backslash (\backslash$$ $100\backslash )$ per unit. Assume that $\backslash ($ A$,$ B$,$ C $\backslash )$ and $\backslash ($ D $\backslash )$ are workers who have different, non$-$interchangeable skills and that each worker is available for only $2,400$ minutes per week $(8$ hours per day, $5$ days per week$).$ For simplicity, assume there's no variation, waste or similar problems in the process. What is the maximum profit$/$week$?$ Explain your decision.

$2.$ If the scrap rate for each process step above is $\backslash (2\backslash \%\backslash )$ each $($box $\backslash ($ A$,$ B$,$ C$,$ D $\backslash )),$ what is the RTY for product $\backslash (\backslash$mathrm$\{$P$\}\backslash$& $\backslash$mathrm$\{$Q$\}\backslash )?$

From The Haystack Symdrome $($North River Press, $1991)$ by Eliyahs M$.$ Goidrart, p$.67$