Problem $2\mathrm{.}25$ from the text.

"Part A is produced in machines $1$ and $2.$ Part B is produced in machines $3$ and $4.$ Parts

A and $B$ are assembled in workstation $5$ to create $C.$ Assembly $C$ is painted in process $6.$

Given the scrap percentages $d1,$dots,$d6$ for each operation and the desired output O$6$ for

C $,$ determine an equation that can be used to calculate the required input $11$ to machine

$1."$

Assume that part A must pass through machines $1$ and $2$ to be completed. For example,

machine $1$ drills a hole and machine $2$ puts a taper in the hole made at machine $1.$

Similarly, part B must pass through both machines $3$ and $4$ to be completed. Please note

that on problem $2\mathrm{.}25$ that "the desired output $06"$ means the output of station $6$ and that

"input $11$ to machine $1"$ is a typo and means the input to machine $1($it ought to read

"input to machine $1").(25$ pts$)$

a$.$ Determine an equation for the required input for both machines $1$ and $3($not just

machine $1$ as stated in the problem.$)$

b$.$ Determine the required input for both machines $1$ and $3$ if the following scrap

percentages apply: $1=\mathrm{.}10,p2=\mathrm{.}05,p3=\mathrm{.}05,p4=\mathrm{.}02,p5=\mathrm{.}04,p6=\mathrm{.}01.$

c$.$ If the desired output of parts at station $6$ is $70$ parts per hour determine the input

rate of parts required at stations $1$ and $3$ for the problem variation described in

part b of this problem.

d$.$ How does the answer to part b change if $75\%$ of the defects at machine $1$ and

$99\%$ of the defects at machine $5$ can be reworked? Give both a qualitative and

quantitative answer $-$ the quantitative answer will relate I $1$ to O $6$ for example but

will not be a number such as start with $100$ parts because no numeric value is

specified for O$6.$