Answer: a). 4,812 hot dogs
b). 16 runs per year
c). 0.96
Step-by-step explanation: Optimal order quantity is found when annual setup cost equals annual holding cost.
Variables;
Q0= Optimal run size
D = Annual demand in units
S = Setup cost per order
H = Holding cost per unit per year
D is not given. So to get D=u×T; u= usage rate = 250 per day; T=300
Therefore D=250×300= 75000
S=$66
H=$0.45 per hot dog
T(year)=300 days
p= production rate5000 per day
a). Optimal run size = Q0 = √2DS/H √p/p-u = √2(75000)66/0.45 ×√5000/5000-250=4,690.41576 × 1.02597835=4,812.26502= 4,812(approximately)
b). Circle time= Q0/u= 4812/250= 19days
Number of runs/year= T(year)/Circe time= 300/19 15.7894737=16(approximately)
c). Runtime= Q0/p= 4812/5000= 0.96