Radovilsky Manufacturing Company, in Hayward, California, makes flashing lights
ID: 367542 • Letter: R
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 12,500 flashing lights per year and has the capability of producing 95 per day. Setting up the light production costs $51. The cost of each light is $0.95. The holding cost is $0.05 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 cot per year?
d) What is the total cost per year, including the cost of the lights?
Please include all the work.
Explanation / Answer
Annual demand(D) = 12500 lights
Demand rate(d) = D/Number of days ina year = 12500/300 = 41.67 or rounded to 42 lights per day
Production rate(p) = 95 lights per day
Setup cost(S) = $51
Holding cost(H) = $0.05
a) Optimal size of production run(Q) = Sqrt of [ (2DS) / {H[1-(d/p)]} ]
= Sqrt of [(2X12500X51) / {0.05[1-(42/95)]} ]
= Sqrt of [(1275000) / (0.05 X0.56) ]
= Sqrt of (1275000 / 0.028)
= 6748 flashlights
b) Imax = (Q/p)(p-d) = (6748/95)(95-42) = 71 x 53 = 3763 lights
Average holding cost per year = (Imax/2)H = (3763/2)0.05 = $94.08
c) Average setup cost per year = (D/Q)S = (12500/6748)51 = $94.47
d) Annual cost of lights =D x Cost per light = 12500 x $0.95 = $11875
Total cost per year = Annual holding cost + Annual setup cost + Annual cost of lights
= $94.08 + $94.47 + $11875
= $12063.55
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