In Example $2\mathrm{.}7,$ suppose $11$ machines are to be assigned. Which of the following assignments will minimize the total cost over a common time period: $\{2,2,2,2,3\}$ or $\{2,2,2,2,2,1\}?$ Is there another combination that will be less expensive?

PRODUCT, PROCESS, AND SCHEDULE DESIGN

Figure $2\mathrm{.}18$ Multiple activity chart for Example $2\mathrm{.}5.$

Excluding idle time, each machine cycle requires $a+t$ minutes to complete a cycle.

Likewise, the operator devotes $a+b$ minutes to each machine during a cycle. Hence, an

ideal assignment is

$n^{\text{'}}=\frac{a+t}{a+b}$

For the example, a equals two minutes, $b$ equals one minute, and $t$ equals six minutes.

Therefore, $n^{\text{'}}$ equals $2\mathrm{.}67$ machines.

Since a fractional number of machines cannot be assigned to an operator, consider

what will happen if some integer number of machines, $m,$ is assigned. The work content