The Friendly Sausage Factory (FSF) can produce hot dogs at a rate of 5,000 per d
ID: 390051 • Letter: T
Question
The Friendly Sausage Factory (FSF) can produce hot dogs at a rate of 5,000 per day. FSF supplies hot dogs to local restaurants at a steady rate of 240 per day. The cost to prepare the equipment for producing hot dogs is $66. Annual holding costs are 45 cents per hot dog. The factory operates 296 days a year.
Find the optimal run size. (Do not round intermediate calculations. Round your answer to the nearest whole number.)
Find the number of runs per year. (Round your answer to the nearest whole number.)
Find the length (in days) of a run. (Round your answer to the nearest whole number.)
The Friendly Sausage Factory (FSF) can produce hot dogs at a rate of 5,000 per day. FSF supplies hot dogs to local restaurants at a steady rate of 240 per day. The cost to prepare the equipment for producing hot dogs is $66. Annual holding costs are 45 cents per hot dog. The factory operates 296 days a year.
Explanation / Answer
Given values:
Daily production (p) = 5,000 per day
Daily demand (d) = 240 per day
Setup cost (S) = $66
Annual holding costs (H) = $0.45 per hot dog
Number of working days = 296 days
Solution:
Annual demand (D) = Daily Demand x Number of working days
Annual demand (D) = 240 x 296
Annual demand (D) = 71,040
(a) Optimal run size (Q) is calculated as,
Q = SQRT [(2 x D x S) / H (1 - d/p)]
Putting the given values in the above formula, we get,
Q = SQRT [(2 x 71,040 x $66) / $0.45 (1 - 240/5000)]
Q = SQRT (9,377,280 / 0.4284)
Q = 4,678.58 or 4,679 (Rounding off to the nearest whole number)
Optimal run size = 4,679 units
(b) Number of runs per year is calculated as,
Number of runs = Annual demand (D) / Optimal run size (Q)
Number of runs = 71,040 / 4,679
Number of runs = 15.18 or 15 (Rounding off to the nearest whole number)
Number of runs = 15
(c) Length of a run is calculated as,
Run length = Optimal run size (Q) / Daily production (p)
Run length = 4,679 / 5,000
Run length = 0.9358 or 1 (Rounding off to the nearest whole number)
Run length = 1 day
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