Question

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 260 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 294 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.)

Answer 1

Answer:

a. 21 327 hot dogs/run

b. 70 runs/yr

c. 4 da/run

Step-by-step explanation:

Data:

Production rate (p)           = 5000/da

Usage rate (u)                  =    260/da

Setup cost (S)                   = $66

Annual carrying cost (H) = $0.45/hot dog

Production days (d)         = 294 da

Calculations:

a. Optimal run size

(i) Annual demand (D) = pd = (5000 hot dogs/1 day) × (294 days/1 yr)

= 1 470 000 hot dogs/yr

(ii) Economic run size

$Q_{0}= \sqrt{\frac{2DS }{ h}\times\frac{ p}{p-u }}$

$= \sqrt{\frac{2\times1470000\times66 }{ 0.45}\times\frac{ 5000}{5000-260 }}$

$= \sqrt{431200000\times\frac{ 5000}{4740 }}$

$= \sqrt{454852321}$

= 21 327 hot dogs/run

b. Number of runs per year

Runs = D/Q₀ = (1 470 000 hot dogs/1yr) × (1 run/21 327 hotdogs)

= 70 runs/yr

c. Length of a run

Length = Q₀/p = (21 327 hot dogs/1 run) × (1 da/5000 hot dogs)

= 4 da/run