The Friendly Sausage Factory (FSF) can produce hot dogs at a rate of 4,500 per d
ID: 347856 • Letter: T
Question
The Friendly Sausage Factory (FSF) can produce hot dogs at a rate of 4,500 per day. FSF supplies hot dogs to local restaurants at a steady rate of 220 per day. The cost to prepare the equipment for producing hot dogs is $62. Annual holding costs are 42 cents per hot dog. The factory operates 292 days a year a. Find the optimal run size. (Do not round intermediate calculations. Round your answer to the nearest whole number) Optimal run size b. Find the number of runs per year. (Round your answer to the nearest whole number.) Number of runs c. Find the length (in days) of a run. (Round your answer to the nearest whole number.) Run length (in days)_Explanation / Answer
Given values:
Daily production, p = 4,500
Daily demand, d = 220
Setup cost, S = $62
Annual holding cost, H = $0.42 per hot dog
Number of working days = 292 days a year
Annual demand, D = 292 x 220 = 64,240
Solution:
(a) The optimal run size is calculated as
Optimal run size = (2*D*S) / H x p / (p-d)
where,
D = Annual demand
S = Setup costs
H = Holding costs
d = daily demand
p = daily production
Putting the given values in the above formula, we get;
Optimal run size (Qo) = (2 x 64240 x 62) / 0.42 x 4500 / (4500 - 220)
Optimal run size (Qo) = 18966095.24 x 1.05
Optimal run size (Qo) = 4355.01 x 1.02
Optimal run size (Qo) = 4442.11
Optimal run size = 4442
(b) Number of runs per year is calculated as;
Number of runs = Annual Demand (D) / Optimal run size (Qo)
Number of runs = 64240 / 4442
Number of runs = 14.46 per year
Number of runs = 15 per year
(c) Length of a run is calculated as;
Run length = Optimal run size (Qo) / Daily production (p)
Run length = 4442 / 4500
Run length = 0.99
Run length = 1 day
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