Problem 10-18 A production process consists of a three-step operation. The scrap

Question

Problem 10-18 A production process consists of a three-step operation. The scrap rate is 14 percent for the first step and 10 percent for the other two steps. a.lf the desired daily output is 460 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 660 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 89 clf 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 $2,000

Explanation / Answer

Let number of units to be started with = 100.N

Therefore , amount of output after three steps

= 100.N x ( 1 – 14/100) x ( 1 – 10/100)x ( 1 – 10/100)

= 100.N x 0.86 x 0.9 x 0.9

= 69.66,N

Since desired daily output = 460 units

Therefore ,

69.66.N = 460

Or, 100.N = 460/69.66 x 100 = 660.35 ( 661 rounded to next whole number )

Note: the answer is 660 if the answer is rounded to nearest whole number. But the answer will be 661 if it is rounded to next whole number which has been asked for.

NUMBER OF UNITS = 661

The revised scrap rates after cutting it by half at every step ::

Step 1 = 7%

Step 2 = 5%

Step 3 = 5%

Let the number of units to be started with to produce an output of 460 units = 100.N1

Therefore ,

100.N1 x ( 1 – 7/100) x ( 1 – 5/100) x ( 1 – 5/100) = 460

Or , 100.N1 x 0.93 x 0.95 x 0.95 = 460

Or, 83.9325.N1 = 460

Or, 100.N1 = 460/83.9325 X 100

Or, 100.N1 = 548.05

Therefore ,

Amount of units which would be saved in terms of scrap allowance

= 660.35 – 548.05

= 112.30 ( 113 rounded to next whole number )

NUMBER OF UNITS = 113

Amount of scrap generated as per original scrap rate

= Input quantity – Output quantity

= 661– 460

= 201

Amount it is costing the company @$10/ unit

= 201 x 10

= $2010

AMOUNT IT IS COSTING THE COMPANY = $2010

Note: The answer would be $2000 if we consider Input quantity of 660. It has been explained why we are not considering 660 as input quantity

NUMBER OF UNITS = 661

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