A production process consists of a three-step operation. The scrap rate is 15 pe

Question

A production process consists of a three-step operation. The scrap rate is 15 percent for the first step and 8 percent for the other two steps.

a.If the desired daily output is 489 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.If 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.If 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.) Cost:

Explanation / Answer

Since scrap rate is 15 percent at first step , output of first step = 100.N x ( 1 – 15/100) = 85.N

85.N is input for the 2nd step. Since scrap rate is 8 percent , output of 2nd step = 85.N x ( 1 – 8/100) =0.92 x 85.N = 78.2N

78.2N is input for the 3rd step . Since scrap rate is 8 percent , output of 3rd step = 78.2N x ( 1 – 8/100 ) = 0.92x 78.2N = 71.944N

Since daily output is = 489 units ,

71.944N = 489

Or, 100.N =( 489/71.944) X 100 = 679.70 ( 680 ROUNDED TO NEXT WHOLE NUMBER )

Number of units = 680 units

Step 1 : 7.5%

Step 2 : 4%

Step 3 : 4%

Let input quantity = 100.N1

Output quantity = 489

The revised calculation as follows :

Since scrap rate is 7.5% percent at first step , output of first step = 100.N1 x ( 1 – 7.5/100) = 0.925X 100.N = 92.5N

92.5N1 is input for the 2nd step. Since scrap rate is 4 percent , output of 2nd step = 92.5.N1 x ( 1 – 4/100) = 0.96 X 92.5N1 = 88.8N1

88.8N1 is input for the 3rd step . Since scrap rate is 4 percent , output of 3rd step = 88.8N1 x ( 1 – 4/100 ) = 0.96 X 88.8N1 = 85.248N1

Therefore ,

85.248.N1 = 489

Or, 100.N1 = ( 489/85.248) X 100

Or, 100.N1 =573.62 ( 574 units rounded to next whole number )

Number of units this would save in terms of scrap allowance

=680 units – 574 units

= 106 units

Number of units this would save in terms of scrap allowance = 106 units

= Input quantity – Output quantity

=680 – 489

= 191 units

Cost of scrap = $10 per unit

Amount it is costing the company per day = $10/ unit x 191 units = $1910

Amount it is costing the company basis original scrap rate = $1910

Number of units = 680 units

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