Question

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?

Answer 1

Answer:

The initial input should be of 566 units to achieve a final output of 450 untis

Explanation:

$\frac{ OUTPU T }{1-scrap} = INPU T$

In this case we have three cycles, the output of the first cycle is the input of the second cycle. Then the output of the second cycle is the input of the third cycle and finally after this cycle we want an output of 450 units:

Output /(1 - scrap_1) = input

input cycle 2 /(1 - scrap_1) = input

input cycle 3 /(1 - scrap_2) = input cycle 2

output cycle 3 /( 1 - scrap_3) = input cycle 3

we wanta final output of 450 untis

and scrap are:

scrap_1   10%

scrap_2    6%

scrap_3    6%

calculations:

450 /(1 - 6%) = input cycle 3

input cycle 3 = 478.7234

478.7234 / (1 - 0.06) = input cycle 2

input cycle 2 = 509.28

509.28 /(1 - 0.10) = input

input = 565,8669  = 566 units