Question

A production process consists of a three-step operation. The scrap rate is 16 percent for the first step and 6 percent for the other two steps. a.If the desired daily output is 485 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 $

Answer 1

Given : Scrap rate of operation 1 =16 %

Let x be the number of units to start the process.

Functional units rate of  operation 1 =100-scrap rate=100-16=84 %

Total functional units =84 % of x

=0.84x

Functional units rate of operation 2 =100-6=94 %

Total functional units after operation 2 =94 % of (Total functional units of after operation 1)

=0.94 *0.84 x

=0.7896x

Similarly ,  

Total functional units after operation 3 =94 % of (Total functional units of after operation 2)

=0.94*0.7896x

=0.74224x

Total number of units after operation 3 =desired daily output=485

i.e 0.74224x=485

x=485/0.74224

=653.44=654 units

The number of units to start the process=x=654 units

b.If the scrap rate is reduced by half at each step

Scrap allowance before reduction=654-485=169

Total number of units after operation 3=0.92*0.97*0.97 x

0.865628x=485

x=560.28=561 units

Total number of scrap units after scrap rate reduction =560.28-485=75.2868

Number of units this would save=168.4415-75.2868=93.15468=94 units

c.Cost of scrap per unit =10

Number of scrap units from part a=653.44-485=168.44

Cost =168.44 *10=1684.4=1684 (rounding to nearest whole number)