Problem $6-1($Algo$)$

An assembly line with $15$ tasks is to be balanced. The longest task is $3$ minutes, and the total time for all tasks is $15$ minutes. The line will operate for $449$ minutes per day.

a$.$ What are the minimum and maximum cycle times? $($Round your answers to $1$ decimal place.$)$

$\backslash$table$[[\backslash$table$[[$Minimum cycle$],[$time$]],3\mathrm{.}0,$minutes$],[\backslash$table$[[$Maximum cycle$],[$time$]],15\mathrm{.}0,$minutes$]]$

b$.$ What range of output is theoretically possible for the line? $($Rour answers to whole numbers.$)$

$\backslash$table$[[,30,\backslash$table$[[$units per$],[$day$]]],[\backslash$table$[[$Minimum$],[$output$]],150,\backslash$table$[[$units per$],[$day$]]],[\backslash$table$[[$Maximum$],[$output$]],,]]$

c$.$ What is the minimum number of workstations needed if the maximum output rate is to be sought? $($Round your answer up to a whole number.$)$

$\backslash$table$[[\backslash$table$[[$Minimum number of$],[$workstations$]]]]$

d$.$ What cycle time will provide an output rate of $128$ units per day? $($Round your answer to $1$ decimal place.$)$

$\backslash$table$[[$Cycle$,$minutes per$],[$cycle$,]]$

e$.$ What output potential will result for the following cycle times? $($Round your answers to whole numbers.$)$

$\backslash$table$[[9$ minutes,$49,\backslash$table$[[$units per$],[$day$]]],[15$ minutes,$30,\backslash$table$[[$unils per$],[$day$]]]]$