Answer:
a. 5218 hot dogs
b. 18 runs per year
c. 1 day per run
Step-by-step explanation:
(a) Let n represent the number of hotdogs in an optimal run. The number of runs needed in a year is ...
r = (260 hotdogs/day)·(365 days/year)/(n hotdogs/run) = 94900/n runs/year
The number of hotdogs in storage decreases from n at the end of a run to 0 just before a run. The decrease is linear, so the average number in storage is n/2.
We can go to the trouble to write the equation for total cost, then differentiate it to find the value of n at the minimum, or we can just jump to the solution. That solution is ...
holding cost = setup cost
(n/2)·0.46 = (94900/n)·66
n^2 = 94900·66·2/0.46 = 27,232,173.9
n ≈ 5218.446
The optimal number of hotdogs in a run is 5218.
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(b) The number of runs needed per year is (from part (a)) ...
r = 94900/5218 ≈ 18.187
The number of runs per year is 18.
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(c) The run lenght is 5218 hotdogs, and the run produces them at the rate of 5500 hotdogs/day, so the run length in days is ...
(5218 hotdogs)/(5500 hotdogs/day) = 0.9487 days
The run length is 1 day.
