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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