b) What is the maximum number of wheel bearings that will be in inventory at Whe
ID: 354202 • Letter: B
Question
b) What is the maximum number of wheel bearings that will be in inventory at Wheel-Rite?
c)How many production runs of wheel bearings will Wheel-Rite have in a year?
d)What is the toal setup plus holding cost for Wheel-Rite?
Arthur Meiners is the production manager of Wheel-Rite, a small producer of metal parts. Wheel-Rite supplies Cal-Tex, a larger assembly company, with 10,000 wheel bearings each year. This order has been stable for some time. Setup cost for Wheel-Rite is $42, and holding cost is $0.70 per wheel bearing per year. Wheel-Rite can produce 520 wheel bearings per day. Cal-Tex is a just-in-time manufacturer and requires that 47 bearings be shipped to it each business day. a) What is the optimum production quantity?units (round your response to the nearest whole number).Explanation / Answer
Given are the following data
Annual demand for wheel bearings with Cal Tex = D = 10,000
Daily demand = d = 47 bearings
Daily production capacity = p = 520 bearings
Set up cost = Cs = $ 42
Annual unit holding cost for bearings = Ch = $ 0.70
Therefore , Optimum production quantity
= Square root ( 2 x Cs x D / Ch x ( 1 – d/p) )
= Square root ( 2 x 42 x 10,000 / 0.70 x ( 1 – 47/520))
= Square root ( 2 x 42 x 10,000 / 0.70 x 0.909)
= 1148.96 ( 1149 rounded to nearest whole number )
OPTIMUM PRODUCTION QUANTITY = 1149 UNITS
Maximum number of wheel bearings that will be inventory at wheel rite
= Optimum production quantity x ( 1 – d/p)
= 1149 x ( 1 – 47/520)
= 1149 x 0.909
= 1044.44 ( 1044 rounded to nearest whole number )
MAXIMUM NUMBER OF WHEEL BEARINGS THAT WILL BE IN INVENTORY AT WHEEL RITE = 1044
Number of production runs wheel rite will have in a year
= Annual demand / Optimum production quantity
= 10,000 / 1149
= 8.703
WHEEL RITES ON AVERAGE WILL HAVE 8.703 PRODUCTION RUNS IN A YEAR
Total annual set up cost
= Set up cost x Number of set ups
= 42 x 8.703
= $365.52
Total annual holding cost
= Annual unit holding cost x Maximum inventory /2
= $0.70 x 1044/2
= $365.40
Total set up plus holding cost = $365.52+ $365.40 = $730.92
TOTAL SET UP PLUS HOLDING COST FOR WHEEL RITE = $730.92
OPTIMUM PRODUCTION QUANTITY = 1149 UNITS
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