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 9,000 flashing lights per year and has the capacity of producing 60 per day. Setting up the light production costs $49. The holding cost is $0.10 per light per year. a. What is the optimal size of the production run?
b. What is the average holding cost per year?
c. What is the average setup cost per year?
d. What is the total cost per year, including the cost of the lights?

a. 2,970

b. $148.50

c. $148.50

d. $297.00

Explanation:

Optimal size of the production run is the size of the Production run that minimizes set -up costs and holding costs.

Optimal size of the production run = √ (2 × Annual Production Demand × Set-up Cost) / Holding Cost per unit

                                                          = √(2 × 9,000 × $49) / $0.10

                                                          = 2,969.85 or 2,970 flashing lights

Average holding cost = Optimal size of the production run /2 × Holding Cost per unit

                                     = 2,970/2 × $0.10                        

                                     = $148.50

Average setup cost = Annual Production Demand / Optimal size of the production run × Cost per set -up

                                = 9,000 / 2,970 × $49

                                = $148.50

Total Cost = Average holding cost + Average setup cost

                 = $148.50 + $148.50

                 = $297.00