Scenario 11.3 - Sammy's Sammwiches
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 a dough is $3 per loaf.Sammy's sells their sandwiches at a rate of fifty per hour.
-What is the cost to run Sammy's at the economic production lot size?

Question

Quizplus · Accepted Answer

First, we need to calculate the economic production lot size, which is the optimal quantity to produce at each batch. We can use the formula:

EOQ = sqrt((2DS)/H)

where:
D = demand rate = 50 sandwiches per hour
S = setup cost = $3 per loaf
H = holding cost = 80% of $1 = $0.80 per loaf per hour

EOQ = sqrt((2x50x3)/0.80) = sqrt(375) = 19.36 or approximately 19 loaves

This means that Sammy's should bake 19 loaves of bread at a time to minimize the total cost of production and inventory.

Now, let's calculate the total cost to run Sammy's at the economic production lot size:

- Cost of bread: $1 per loaf x 19 loaves = $19
- Holding cost: $0.80 per loaf per hour x 19 loaves x 0.5 hour (since we assume half of the bread is held in inventory before selling) = $7.60
- Setup cost: $3 per batch = $3
- Total cost: $19 + $7.60 + $3 = $29.60
- Cost per sandwich: $29.60 / 50 sandwiches = $0.592 or approximately $0.59

Therefore, the cost to run Sammy's at the economic production lot size is $0.59 per sandwich, which is option B.