Which of the four processing stations has the highest aggregate workload, and therefore, is the bottleneck in the production of doors at Olde World?

The company cannot always meet the demand for its doors, so the management team must make decisions about what quantities of each door it should produce to maximize profits. Because each of the three door styles has different costs and margins, Olde World has been prioritizing production by using a traditional method of accepting as much of the product with the highest margins up to the demand limit first, and then filling in the production plan with the next most profitable door and then the least profitable door. However, the Theory of Constraints $($TOC$)$ may suggest a way to improve profitability.

How would profits be improved if a TOC$/$bottleneck$-$based method for scheduling were used to determine the product mix? Show calculations for both the traditional and TOC$/$bottleneck methods.

Explain why the TOC$/$bottleneck method is or is not superior for optimizing the profitability of the product mix.