Question

A production process consists of a three-step operation. The scrap rate is 20 percent for the first step and 12 percent for the other two steps.

a.If the desired daily output is 461 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

SOLUTION :

let us start from 1000 units

step -1 = 20 % scrap rate  

= 1000 * 80 %

= 800 units

step -2 = 12% scrap rate

= 800 * 88%

= 704 units

step - 3 = 12 % scrap rate

= 704 * 88%

= 619.52

* 619.52 units out put when there is 1000 units available

* 1 unit output when there is 1000 / 619.52 units available

* so 461 units output when there is

= (1000/619.52 ) * 461

= 1.614 * 461

= 744.054

(B )

SCRAP rate is half , drive the no of units as follows

step - 1 10% scrap rate

= 1000* 90%

= 900 units

step -2 6% scrap rate

= 900 * 94%

= 846 units

step -3 6 % scrap rate

= 846 * 94 %

= 795.24 units

795.24 units for 1000 units

for 461 units = 461 * (1000 / 795.24)

= 461 * 1.25

= 576.25

hence the number of units saved =( 744.05 - 576.25 )

= 167 . 8 units

( C )

SCRAP COST = ( ORIGINAL NUMBER OF UNITS - OUT PUT ) * SCRAP COST

= ( 744 . 05 - 461 ) * 10 $

= ( 283.05) * 10

= $ 2830 .5

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