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Part $1$

$$Yost$-$Perry Industries$($YPI$)$ manufactures a mix of affordable guitars$($A$,$ B$,$ C$)$ that are fabricated and assembled at four different processing stations$($W$,$ X$,$ Y$,$ Z$).$ The operation is a batch process with small setup times that can be considered negligible. The product information$($price$,$ weekly$$ demand, and processing$$ times$)$ and process sequences are shown below. Purchased parts and raw materials$($shown as a$$ 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$$ $$9,000/$week$.$

$$11$

$$8$

$$4$

$$5$

Step $1$

Step $1$

Station W

Station W

Step $2$

Step $2$

Station Y

Station Z

Product A

Product B

Raw materials

Raw materials

$(13$ min$)$

$(8$ min$)$

$(13$ min$)$

$(10$ min$)$

Purchased part

Step $1$

Product C

Step $2$

Station X

Purchased part

Purchased part

Raw materials

Station W

$$14$

$$5$

$(20$ min$)$

$(9$ min$)$

In the diagram, a flowchart represents the manufacturing process of products A$,$ B$,$ and C in different rows. From top to bottom, rows are arranged for Product A$,$ Product B$,$ and Product C$,$ respectively. Each row begins with an inverted triangle containing the dollar amount for the raw materials that go into the process. An arrow that emerges from the triangle is followed to the right by a series of rectangles for each step in the process. Each rectangle contains the step number, station name where that step takes place, and duration in minutes for that step. Between steps $2$ and $3,$ each process has a purchased part added to the flow as indicated by an inverted triangle with the dollar amount for the purchased part inside. The final step in each process is followed by an arrow to a summary process that shows the product name, price per unit, and demand in units per week for that product. For product A$,$ a value of $$11$ is displayed inside the initial triangle. For Step $1,$ Station W is used and the step takes $13$ minutes. For Step $2,$ Station Z is used and the step takes $10$ minutes. After step $2,$ a purchased part costing $$5$ is added to the flow. For Step $3,$ Station X is used and the step takes $9$ minutes. The final output arrow points to summary process that reads Product: A$,$ Price: $$105$ per unit, and Demand: $66$ units per week. For product B$,$ a value of $$8$ is displayed inside the initial triangle. For Step $1,$ Station W is used and the step takes $8$ minutes. For Step $2,$ Station Y is used and the step takes $13$ minutes. After step $2,$ a purchased part costing $$4$ is added to the flow. For Step $3,$ Station Z is used and the step takes $8$ minutes. The final output arrow points to summary process that reads Product: B$,$ Price: $$95$ per unit, and Demand: $80$ units per week. For product C$,$ a value of $$14$ is displayed inside the initial triangle. For Step $1,$ Station X is used and the step takes $9$ minutes. For Step $2,$ Station W is used and the step takes $20$ minutes. After step $2,$ a purchased part costing $$5$ is added to the flow. For Step $3,$ Station Y is used and the step takes $5$ minutes. The final output arrow points to summary process that reads Product: C$,$ Price: $$110$ per unit, and Demand: $66$ units per week.

Step $3$

Step $3$

Station X

Station Z

Product: A

Product: B

$(9$ min$)$

$(8$ min$)$

Price: $$105/$unit

Demand: $66$ units$/$wk

Demand: $80$ units$/$wk

Price: $$95/$unit

Step $3$

Station Y

$(5$ min$)$

Product: C

Price: $$110/$unit

Demand: $66$ units$/$wk

x y graph

Part $2$

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

$$

Workstation W

Workstation X

Workstation Y

Workstation Z

$,$ with a total load time of

$$

enter your response here minutes. $($Enter your response as an$$ integer.$)$