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 10 percent for the other two steps. a.If the desired daily output is 473 units, how many units must be started to allow for loss due to scrap? 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

Answer to question a :

Let the input quantity = 100.N

Therefore output after first step ( scrap rate 15 percent ) = 85.N

Output at 2nd step ( 10 percent scrap rate ) with output of first step acting as input = 90% of 85.N = 76.5.N

Output at 3rd step ( 10 percent scrap rate) with output of 2nd step acting as input = 90% of 76.5,N = 68.85.N

Thus when input is 100.N, output will be 68.85.N

Thus corresponding input for desired daily output of 473 units = 100/68.85   x 473 units = 687 units

NUMBER OF UNITS = 687 UNITS

Answer to question b :

With scrap rate at every stage cut into half of original one , the revised calculation as follows :

Let the input quantity = 100.N

Therefore output after first step ( scrap rate 7.5 percent ) = 92.5.N

Output at 2nd step ( 5 percent scrap rate ) with output of first step acting as input = 95% of 92.5.N = 87.875.N

Output at 3rd step ( 5 percent scrap rate) with output of 2nd step acting as input = 95% OF 87.875.N = 83.48N

Thus when input is 100.N, output will be 83.48.N

Thus corresponding input for desired daily output of 473 units = 100/83.48   x 473 units = 566.60

Therefore , number of units it will save = 687 - 566.60 = 120.40 ( 121 rounded to next whole number )

NUMBER OF UNITS = 121

Answer to question c :

Amount of scrap units ( as calculated in a ) = 687 – 473 = 214 units

Therefore , amount it is costing the company per day ( @ 10 / unit ) = $10 / unit x 214 units = $2140

COST = $2140

NUMBER OF UNITS = 687 UNITS

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.