Problem $3.$

Yost$-$Perry Industries $($YPI$)$ manufactures a mix of affordable guitars $(A,B,C)$ that are fabricated and assembled at four different processing stations $(W,x,Y,Z).$ The operation is a batch process with small setup times that can be considered negligible. The product information $($price$,$ weekly demand, and processing times$)$ and process sequences are shown in figure below. Raw materials and purchased parts $($shown as a per$-$unit consumption rate$)$ are represented by inverted triangles. YPI is able to make and sell up to the limit of its demand per week with no penalties incurred for not meeting the full demand. Each workstation is staffed by one highly skilled worker who is dedicated to work on that workstation alone and is paid $$15$ per hour. The plant operates one $8-$hour shift per day and operates on a $5-$day work week $($i$.$e$.,40$ hours of production per person per week$).$ Overhead costs are $9$ n $0$ n$/$week

a$)$ Which of the four workstations, W$,$ X$,$ Y$,$ or Z$,$ has the highest aggregate workload, and thus serves as the bottleneck for YPI?

b$)$ Yost$-$Perry Industries' $($YPI$)$ senior management team wants to improve the profitability of the firm by accepting the right set of orders. Currently, decisions are made using the traditional method, which is to accept as much of the highest contribution margin product as possible $($up to the limit of its demand$),$ followed by the next highest contribution margin product, and so on until all available capacity is utilized. Because the firm cannot satisfy all the demand, the product mix must be chosen carefully. Jay Perry, the newly promoted production supervisor, is knowledgeable about the theory of constraints and the bottleneck$-$based method for scheduling. He believes that profitability can indeed be improved if bottleneck resources are exploited to determine the product mix. What is the change in profits if$,$ instead of the traditional method that YPI has used thus far, the bottleneck method advocated by Jay is used for selecting the product mix?