Question

Please answer both questions. Show work

Sammy's is the hot new lunch spot among the hipsters, who flock there at noon for their artisanal peanut butter and jelly sandwiches, which sell for $12.95. The sandwiches are made from two slices of their own artisanal bread, which they bake continuously throughout the day at a rate of seven loaves an hour (each loaf contains twenty slices). The actual cost of a loaf of bread is $1 and the cost to hold a loaf is 80%, since freshness is important in baking as well as to hipsters. The cost to run a new batch of dough is $3 per loaf. Sammy's sells their sandwiches at a rate of fifty per hour.

A. What is the optimal batch size to produce?

B. What is the cost to run Sammy's at the economic production lot size?

Answer 1

Daily selling rate for Sammy = d = 50 sandwiches per hour

Daily production rate = p = seven loaves /hour or140 slices per hour = 70 sandwiches per hour

Annual demand of sandwich = 50 sandwich. Per hour or 50 x 24 x 365 = 438000sandwiches a yar

1 loaf = 20 slices = 10 sandwiches

Annual unit holding cost per loaf of bread =I =   80% of $1= 0.8 $ per loaf of bread = 0.08$ per unit of sandwich

Set uo cost = S = $3 per loaf = $0.3 per sandwich

Optimal batch size to produce = Square root ( 2 x D x S/I ( p/p-d)

= square root ( 2 x 438000 X$0.3 /0.08 x ( 70 / 70 – 50))

= 3390.79 SANDWICHES

Annual cost of sandwich = 438000 x $12.95 = $5672100

Annual set up cost = Set up cost x Annul demand /order qty of sandwich = $0.3 x 438000/3390.79 = $38.75

Annual inventory holding cost = I x order quantity /2 = $0.08 x 3390.79/2= $135.63

Cost to run at economic production quantity =$5672100 + $38.75 +$135.63 = $5672274.38