Canine Kennels Company$($CKC$)$ manufactures two different types of dog chew toys$($A and$$ B$,$ sold in$1,000-$count boxes$)$ that are manufactured and assembled on three different workstations$($W$,$ X$,$ and$$ Y$)$ using a$$ small$-$batch process$($see the figure$$ below$).$ Batch setup times are negligible. The flowchart denotes the path each product follows through the manufacturing$$ process, and each$$ product's price, demand per$$ week, and processing times per unit are indicated as well. Purchased parts and raw materials consumed during production are represented by inverted triangles. CKC can make and sell up to the limit of its demand per$$ week; no penalties are incurred for not being able to meet all the demand. Each workstation is staffed by a worker who is dedicated to work on that workstation alone and is paid$$ $$6$ per hour. Total labor costs per week are fixed. Variable overhead costs are$$ $$3,500/$week$.$ The plant operates one$8-$hour shift per$$ day, or $40$ hours$/$week$.$

$$2$

$$6$

$$5$

$$3$

Step $1$

Step $1$

Station W

Station X

Step $2$

Step $2$

Station W

Station X

Product A

Product B

Raw materials

Raw materials

$(11$ min$)$

$(19$ min$)$

$(15$ min$)$

$(11$ min$)$

Purchased part

Purchased part

In the diagram, a flowchart represents the manufacturing process of products A and B in different rows. From top to bottom, rows are arranged for Product A and Product B$,$ 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 $$2$ is displayed inside the initial triangle. For Step $1,$ Station W is used and the step takes $11$ minutes. For Step $2,$ Station X is used and the step takes $11$ minutes. After step $2,$ a purchased part costing $$3$ is added to the flow. For Step $3,$ Station Y is used and the step takes $18$ minutes. The final output arrow points to summary process that reads Product: A$,$ Price: $$55$ per unit, and Demand: $80$ units per week. For product B$,$ a value of $$6$ is displayed inside the initial triangle. For Step $1,$ Station X is used and the step takes $19$ minutes. For Step $2,$ Station W is used and the step takes $15$ minutes. After step $2,$ a purchased part costing $$5$ is added to the flow. For Step $3,$ Station Y is used and the step takes $10$ minutes. The final output arrow points to summary process that reads Product: B$,$ Price: $$65$ per unit, and Demand: $75$ units per week.

Step $3$

Step $3$

Station Y

Station Y

Product: A

Product: B

$(18$ min$)$

$(10$ min$)$

Price: $$55/$unit

Demand: $80$ units$/$wk

Demand: $75$ units$/$wk

Price: $$65/$unit

x y graph

Part $2$

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

$$

Workstation W

Workstation X

Workstation Y

$,$ with a total load time of

$$

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