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)

Answer 1

a. The Optimal run size is 5,086 hot dogs

b. The Number of runs per year is 18

c. The Run length is 1 day

Step-by-step explanation:

a. According to the given data we have the following:

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

So, Optimal run-size can be calculated as follows:

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 = 5,086

Therefore, Optimal run size is 5,086 hot dogs

b) The Number of runs per year can be calculated as follows:

Cycle time = Q / u

Cycle time = 5086 / 310 = 16 days

Number of runs = Tyear / cycle time

Number of runs = 295 / 16 = 18

The Number of runs per year is 18

c) The Run length or run time can be calculated as follows:

Run time = Q / p

Run time = 5086 / 4500

Run time = 1.13 = 1

Run length is 1 day