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Edit View History Bookmarks Window Help a newco Blackboard@UHD IUniversity of Houston-Downtown pter 13 Homework Saved 3 Problem 13-9 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 270 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 291 days a year. ints a. Find the optimal run size. (Do not round intermediate calculations. Round your answer to the nearest whole number.) size eBook References 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 = 5,000
Daily demand, d = 270
Setup cost, S = $66
Annual holding cost, H = $0.45 per hot dog
Number of working days = 291 days a year
Annual demand, D = 291 x 270 = 78,570
Solution:
(a) The optimal run size is calculated as;
Optimal run size = SQRT [(2*D*S) / H] x SQRT [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) = SQRT [(2 x 78570 x 66) / 0.45] x SQRT [5000 / (5000 - 270)]
Optimal run size (Qo) = SQRT (23047200) x SQRT (1.057)
Optimal run size (Qo) = 4800.7499414 x 1.02810505
Optimal run size (Qo) = 4935.6753
Optimal run size = 4936
(b) Number of runs per year is calculated as;
Number of runs = Annual Demand (D) / Optimal run size (Qo)
Number of runs = 78570 / 4936
Number of runs = 15.92 per year
Number of runs = 16 per year
(c) Length of a run is calculated as;
Run length = Optimal run size (Qo) / Daily production (p)
Run length = 4936 / 5000
Run length = 0.9872
Run length = 1 day
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