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 19 percent for the first step and 11 percent for the other two steps. a.lf the desired daily output is 481 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 $10 per unit, how much is it costing the company per day for the original scrap rate (le. the Part a scrap rate)? (Round your final answer to the nearest whole number. Omit the "$" sign in your response.)

Explanation / Answer

a)

let the initial units started be x

after 1st step: x*19% is scrap, hence x*81% = 0.81x is moved forward to next step

2nd step scrap rate is 11%. hence 89% moves forward = 0.81x*89% = 0.81*0.89x = 0.7209x

3rd step scrap rate is 11%, 89% is the final output = 0.7209x*89% = 0.7209*0.89x = 0.641601x

now the final output required = 481 units

0.641601x = 481

x = 481/0.641601

x= 749.69 = 750 units

b)

if scrap rate is half, 1st step = 19/2 = 9.5%

2nd step = 11/2 = 5.5%

3rd step = 11/2 = 5.5%

units required to produce 481 units = 90.5%*94.5%*94.5%*x

0.905*0.945*0.945x = 481

0.8082x = 481

x = 481/0.8082 = 595.15 = 595 units

units saved = 750-595 = 155 units

c)

cost of scrap = $10

orginal scrap = 750-481 = 269 units

cost = 269*10 = $2690

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