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 12,400 flashing lights per year and has the capability of producing 105 per day. Setting up the light production costs ?$49. The cost of each light is $1.05. The holding cost is ?$0.05 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?

c) What is the average setup cost per year?

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

Answer 1

Annual demand (D) = 12400 lights

Setup cost (S) = $49

Holding cost (H) = $0.05

Daily production rate(p) = 105

Daiky demand rate (d) = D/number of days per year = 12400/300 = 41.33

a) Optimal run size(Q) = sqrt of {2DS/H [1-(d/p)]}

= sqrt of {(2x12400x49)/0.05[1-(41.33/105)]}

=sqrt of (1215200/0.03)

= sqrt of 40506667

= 6364 lights

b) Imax = (Q/p) (p-d) = (6364/105)(105-41.33) = 60.61 x 63.67 = 3859

Holding cost per year = (Imax/2)H = (3859/2)0.05 = $96.48

C) Setup cost per year = (D/Q) S = (12400/6364)49 = $95.47

d) cost of lights = D x cost per light = 12400 x $1.05 = $13020

Total cost = Holding cost + Setup cost + cost of lights

= $96.48 + $95.47 + $13020

= $13211.95