Question

13.2 The Hatchipets Factory can produce toy eggs at a rate of 5,250 per day. Hatchipets supplies toy eggs to local toy stores at a steady rate of 380 per day. The cost to prepare the equipment for producing toy eggs is $67. Annual holding costs are 49 cents per egg. The factory operates 289 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.)
  
Run length (in days)            

Answer 1

Production rate, p = 5,250 per day
Demand rate, d = 380 per day
Cost of setup, K = $67
Carrying cost, h = $0.49 per annum

So, annual demand, D = 380 x 289 = 109,820 units

(a)

Optimal run size = (2.D.K.p / h.(p - d))^1/2 = sqrt(2*109820*67*5250 / (0.49*(5250 - 380))) = 5,690 units

(b)

Number of runs per year = D / Optimal run size = 109820 / 5690 = 19

(c)

Length of a run = Optimal run size / p = 5690 / 5250 = 1.08 or 1 day