Swatville Sluggers is a small manufacturer

Swatville Sluggers is a small manufacturer of baseball bats made from
high quality
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.

Component

Cost ($/unit)

Required for 30 – inch bat

Wood (oz)

0.12

30

Lathe (min)

0.06

10

Finishing Time (min)

0.03

25

Stain (oz)

0.25

2

Varnish (oz)

0.2

5

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 well known
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?

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