Question

the friendly sausage factory can produce hot dogs at a rate of 5000 per day. FSF supplies hot dogs to local restaurants at a steady rate of 330 per day. the cost to prepare the equipment for producing hot dogs is $62. annual holding costs are 47 cents per hot dog. the factory operates 297 days a year. find the optimal run size. find the number of runs per year. find the length in days of a run.

Answer 1

Solution:

(a) Optimal run size (Q):

Q = SQRT [(2 x D x S) / H x (1 - d/p)]

where,

D = Annual demand = Daily demand x Number of working days per year

S = Setup cost

H = Holding cost

d = Daily demand

p = Daily production

Putting the given values in the above formula, we get,

Q = SQRT [(2 x 330 x 297 x $62) / $0.47 x (1 - 330/5,000)]

Q = 5,261.67 or 5,262 (Rounding off to the nearest whole number)

Optimal run size (Q) = 5,262 units

(b) Number of runs:

Number of runs = Annual demand / Optimal run size

Number of runs = (330 x 297) / 5,262

Number of runs = 18.63 or 19 (Rounding off to the nearest whole number)

Number of runs = 19 runs per year

(c) Run length:

Run length = Optimal run size / Daily production

Run length = 5,262 / 5,000

Run length = 1.05 or 1 (Rounding off to the nearest whole number)

Run length = 1 day