Problem $8\mathrm{.}9($Algo$)$

An assembly line is to be designed to operate $7$ hours per day and supply a steady demand of $350$ units per day. Here are the tasks and their performance times:

$\backslash$table$[[$TASK$,\backslash$table$[[$PRECEDING$],[$TASKS$]],\backslash$table$[[$PERFORMANCE TIME$],[($SECONDS$)]],$TASK,PRECEDING,PERFORMANCE TIME$],[$a$,-,20,g,d,($SECONDS$)],[$a$,-,46,h,e,26],[$b$,-,38,i,f,36],[c,-,43,j,g,8],[d,a,18,k,h,i,6],[e,b,8,1,j,k,18],[f,c,,,33,]]$

b$.$ What is the workstation cycle time required to produce $350$ units per day?

Workstation cycle time

seconds per unit

c$.$ What is the theoretical minimum number of workstations?

Note: Round up your answer to the next whole number.

Minimum number of workstations

$$

$$

$\backslash$table$[[$Work Station,Task,Idle Time$],[$I$,b-a,9],[$II$,$d$-$e$,14],[$III$,c-g,1],[$IV$,h-f-i-j,9],[$V$,k-$I,$42]]$

e$.$ What is the efficiency of your line balance, assuming it is running at the cycle time from part $($b$)?$ Note: Round your answer to $1$ decimal place.

Efficiency

f$.$ Suppose demand increases by $10$ percent. How would you react to this? Assume you can operate only $7$ hours per Note: Round your answers to the nearest whole number.

cycle time to

seconds per unit. Another option is to work

$5$ minutes overtime