The Friendly sausage Factory (FSF) can produce hot dogs at a rate of 5000 per day. FSF supplies hot dogs to local restaurants at a steady rate of 250 per day. The cost to prepare the equipment for producing hot dogs is $66. Annual holding costs are 45 cents per hot dogs. The factory operates 300 days a year. Find
a) The optimal run size
b) The number of runs per year
c) The length (in days) of a run

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

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,