Question

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 11,900 flashing lights per year and has the capability of producing 95 per day. Setting up the light production costs $49. The cost of each light is $0.95.The holding cost is $0.10 per light per year.

​a) What is the optimal size of the production​ run? _ units ​(round your response to the nearest whole​ number).

​b) What is the average holding cost per​ year? ​(round your response to two decimal​ places).

​c) What is the average setup cost per​ year? ​(round your response to two decimal​ places).

​d) What is the total cost per​ year, including the cost of the​ lights? ​(round your response to two decimal​ places).

Answer 1

Annual demand (D) = 11900 lights

Set up cost(S) = $49

Holding cost (H) = $0.10

Production rate (p) = 95 lights per day

Demand rate (d) = D/number of days per year = 11900/300 = 39.667 lights per day

Cost per light(C) = $0.95

A) Optimum production quantity(Q) = sqrt of {2DS / H [1-(d/p)]}

= sqrt of {(2x11900x49) /0.10[1-(39.667/95)]}

= Sqrt of [1166200 / 0.10(1-0.4175) ]

= sqrt of [1166200/(0.10 x 0.5825)]

= sqrt of (1166200/0.05825)

= Sqrt of 20020600.8583

= 4474 lights

B) I - max = (Q/p) (p-d) = (4474/95)(95-39.667) = 47.09 x 55.333 = 2605.63 lights

Average holding cost per year =  [(I-max / 2) H] = (2605.63/2)0.10 = $130.28

C)Average setup cost per year = (D/Q) S = (11900/4474)49 = $130.33

D) Cost of lights per year = D x C = 11900x$0.95 = $11305

Total cost per year = Holding cost + setup cost + cost of lights

= $130.28 + $130.33 + $11305

= $11565.61