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 15 percent for the first step and 12 percent for the other two steps. a.If the desired daily output is 454 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

a)

let the initial units started be x

after 1st step: x*15% is scrap, hence x*85% = 0.85x is moved forward to next step

2nd step scrap rate is 12%. hence 88% moves forward = 0.85x*88% = 0.85*0.88x = 0.748x

3rd step scrap rate is 12%, 88% is the final output = 0.748x*88% = 0.748*0.88x = 0.65824x

now the final output required = 454 units

0.65824x = 454

x = 454/0.65824

x= 689.72 = 690 units

b)

if scrap rate is half, 1st step = 15/2 = 7.5%

2nd step = 12/2 = 6%

3rd step = 12/2 = 6%

units required to produce 454 units = 92.5%*94%*94%*x

0.925*0.94*0.94x = 454

0.81733x = 454

x = 454/0.81733 = 555.47 = 555 units

units saved = 690-555 = 135 units

c)

cost of scrap = $10

orginal scrap = 690-454 = 236 units

cost = 236*10 = $2360

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