Suppose that in the inventory problem, the storage cost depends on the maximum inventory size, rather than the average. In this case, the number of units that should be ordered or manufactured to minimize the total cost is $q=\sqrt[\phantom{2}]{\frac{fM}{k}}.$

A book publisher wants to know how many times a year a print run should be scheduled. Suppose it costs $$1000$ to set up the printing process, and the subsequent cost per book is so low it can be ignored. Suppose further that the annual warehouse cost is $$6$ times the maximum number of books stored. Assuming $5400$ copies of the book are needed per year, how many books should be printed in each print run?

The publisher should print $$ books in each print run.

$($Type a whole number.$)$