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A production process consists of a three-step operation
A production process consists of a three-step operation. The scrap rate is 10 percent for the first step and 6 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 _566________
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 $10 per unit, how much is it costing the company per day for the original scrap rate (i.e. the Part a scrap rate)? (Round your answer to the nearest whole number. Omit the "$" sign in your response.)
Cost$ __1160_________
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Expert Solution
Given,
Scrap rate of step 1 = 10%, therefore efficiency is 0.90
Similarly, efficiency of step 2 and 3 are (1-6%) = 0.94
a) Computation of Number of Units must be started to allow for loss due to scrap:
Input = Output/ Efficiency and Input of a step = Output of previous step
Output of step 3 = 450
Input of step 3 = output of step 2 = 450/0.94 = 478.72
Input of step 2 = output of step 1 = 478.72/0.94 = 509.28
Input of step 1 = 509.28/0.90 = 565.87 or 566 units
b) Computation of Number of Units this would save in terms of the scrap allowance:
If scrap rate is cut into half, scrap rates of step 1,2 and 3 are 5%, 3% and 3% respectively.
Accordingly, efficiencies are 95%, 97% and 97% respectively
Therefore, inputs required are ((450 / 0.97) / 0.97) / 0.95 = 503.44 or 503 units
Therefore, Savings in scrap = 566 - 503 = 63 units
c) Computation of Cost of Scrap:
Total units input = 566
Total output = 450
Scrappage = 566 - 450 = 116 units
Therefore, cost of scrap at the rate of $10 per unit = $10* 116 = $1160 per day
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