Radovilsky Manufacturing Company, in Hayward, California, makes flashing lights for toys. The company operates its production facility 300 days per year. It has orders for about 12,500 flashing lights per year and have the capability of producing 100 per day. Setting up the light production costs of $51. The cost of each light is $1.05. The holding cost is $0.10 per light per year. What is the optimal size of the production run? What average holding cost per year? - What is the average setup cost per year? What is the total cost per year, including cost of the lights?

Given Demand D = 12,500 lights per year

Set up cost S = $51

Cost of each light (C) = $1.05

Holding cost = $0.1 per light per year

Production p = 100 lights per day

Usage (d) = 12,500/300 days = 41.66 (round up to 42)

= 42 lights per day

a) What is the optimal sizeof the production run?

Q = √{ (2*D*S) / (H (1 - (d / p))) }

Q = √{ (2*12500*51) / (0.1 (1 - (42/100))) }

= 4688.577 = 4689 units

Q = 4689 units

b) What is the average holding cost per year?

Average holding cost per year = average inventory level * H

= (Q/2) H[1 - (d/p) ]

= (4689/2) 0.1[1 - (42/100) ]

= $135.98

c) What is the average setup cost per year?

average setup cost per year = (D/Q) S

= (12,500/4689) * 51

= 135.97

d) What is the total cost per year, including the cost of the lights?

Total cost = D*C + total set up cost + total holding cost

12,500 * 1.05 + 135.98 + 135.97

Total cost = $ 13,396.95