An airline has 20 planes, is short on money, and doesn't want to spend any more than necessary to keep the planes safely flying. The cost to perform preventive maintenance (PM) on all 20 planes is $16,000. If a plane has a malfunction between PM inspections, it costs an average of $4000 to fix it. The malfunction history on the planes is as follows:
Months between PM Probability of malfunction
One .2
Two .3
Three .5
How often should PM occur to minimize the total expected costs?