Swatville Sluggers is a small manufacturer of baseball bats made from highquality 3-by-3-inch blocks of wood. Once the wood is obtained, it is processed on a lathe, finished, and coated with stain and varnish. The table below provides information about the quantities and variable costs of each of those steps for a 30-inch bat. For example, each bat requires 30 inches of wood that cost $0.12 per inch, 10 minutes of lathe time at $0.06 per minute, and so forth. The sales price is $35.00. Finally, there is a $3 fixed production cost per bat and each bat is put in a box that costs $0.50.
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Component
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Cost ($/unit)
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Required for 30- inch bat
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Wood (oz)
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0.12
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30
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|
Lathe (min)
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0.06
|
10
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Finishing Time (min)
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0.03
|
25
|
|
Stain (oz)
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0.25
|
2
|
|
Varnish (oz)
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0.2
|
5
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a. Swatville has been approached by Avisail Garcia, an up-and-coming player with the Chicago White Sox, to design a new bat for him. Designing a new bat for a wellknown player will pay off in brand recognition for their aluminum bat lines sold to high school and little league baseball teams. It will cost Swatville roughly $5,000 to design the new bat, but they estimate that over the next year they will see an increase in profits of $3000 on their aluminum bat lines from the increased brand recognition. How many bats would Avisail Garcia himself have to purchase in order for this to be an attractive proposition?
b. Ash (the type of wood used to make bats) is in short supply, so the cost of wood has increased to $0.20 per unit. How does this change your recommendation in part a?