In a textile plant, automatic running time for machines is exponentially distributed with a mean of 45 minutes; service time is exponentially distributed with a mean of 5 minutes.

One operator is to be assigned to a specified number of machines. Using the notation in Section 10.9, C1  $90/machine-hour, C2  $45/machine-hour, and C3  C4 

$18/operator-hour. Determine the economic number of machines to assign an operator.