A production process consists of a three-step operation. The scrap rate is 11 pe
ID: 419831 • Letter: A
Question
A production process consists of a three-step operation. The scrap rate is 11 percent for the first step and 11 percent for the other two steps. a.If the desired daily output is 450 units, how many units must be started to allow for loss due to scrap? (Do not round intermediate calculations. Round up your final answer to the next whole number.) Number of units b.lf the scrap rate for each step could be cut in half at every operation, how many units would this save in terms of the scrap allowance? (Do not round intermediate calculations. Round up your final answer to the next whole number.) Number of units c.lf the scrap represents a cost of $10 per unit, how much is it costing the company per day for the original scrap rate (i.e. the Part a scrap rate)? (Round your final answer to the nearest whole number. Omit the "$" sign in your response.) CostExplanation / Answer
Basis 11 percent scrap rate in each of the three successive steps .
Output generated from 100.N input
= 100.N x ( 1 – 11/100)^3
= 100.N x ( 0.89)^3
=100.N x 0.7049
= 70.49.N
Since desired daily output is 450 units ,
70.49N = 450
Or, 100.N = 450/70.49 x 100 = 638.388 ( 639 rounded to next whole number )
NUMBER OF UNITS = 639
Therefore ,
Output generated from 100N input = 100.N( 1 – 5.5/100)^3 = 100N x (0.945)^3 = 84.39.N
Since desired output rate is 450 units,
84.39.N = 450
Or, N = 450 / 84.39 X 100 = 533.23 ( 534 rounded to next higher whole number )
Therefore, number of units it will save in terms of scrap allowance
= 639 units – 534 units
= 105 units
NUMBER OF UNITS = 105
= Input quantity – Output quantity
= 639 – 450
= 189 units
Cost of scrap = $10/ unit
Amount it is costing the company per day = $ 10 / unit x 189 units = $1890 units
COST = $1890
NUMBER OF UNITS = 639
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