MATH SOLVE

4 months ago

Q:
# 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 sizeb. find the number of runs per year. (round your answer to the nearest whole number.) number of runsc. find the length (in days) of a run. (round your answer to the nearest whole number.)

Accepted Solution

A:

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
[tex]Q_{0}= \sqrt{\frac{2DS }{ h}\times\frac{ p}{p-u }}[/tex][tex]= \sqrt{\frac{2\times1470000\times66 }{ 0.45}\times\frac{ 5000}{5000-260 }}[/tex]
[tex]= \sqrt{431200000\times\frac{ 5000}{4740 }}[/tex][tex]= \sqrt{454852321}[/tex]= 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