The Friendly Sausage Factory (FSF) can produce hot dogs at a rate of 4,500 per d
ID: 367982 • 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 310 per day. The cost to prepare the equipment for producing hot dogs is $60. Annual holding costs are 45 cents per hot dog. The factory operates 295 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
To be calculated:
a) Optimal Run size
b) Number of runs per year
c) Run length in days
Given Values:
Daily production, p = 4500 per day
Daily demand, u = 310 per day
Number of working days in a year, Tyear = 295 days
Annual demand, D = Daily demand x number of working days; D = 310 x 295; D = 91450
Setup cost, S = $60
Annual holding cost, H = $0.45 per hot dog
a) Optimal run-size can be calculated as;
Q* = 2 x annual demand x Setup cost / holding cost per unit per year x daily production / daily production - daily demand
Q* = 2DS / H x p / p-u
Q* = ( 2 x 91450 x 60 / 0.45) x ( 4500 / 4500 - 310)
Q* = (24386667) x (1.07)
Q* = (4938.29) x (1.03)
Q* = 5086.44 = 5086
Optimal run size is 5086 hot dogs
b) Number of runs per year can be calculated as;
Cycle time = Q / u
Cycle time = 5086 / 310 = 16 days
Number of runs = Tyear / cycle time
Number of runs = 295 / 16 = 18
Number of runs per year is 18
c) Run length or run time can be calculated as;
Run time = Q / p
Run time = 5086 / 4500
Run time = 1.13 = 1
Run length is 1 day
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