As the operations manager, you are responsible for the maintenance of the main conveyor line that operates throughout the distribution center. The historical frequency of breakdowns of the conveyer per month is noted in the below table. The cost of breakdown repair is $$5,575$ per instance and the cost of preventative maintenance is $$7,620$ per month $($daily inspections, cleaning, lubrication, tightening bolts, and possible parts changes$).$ If preventative maintenance is performed, the probability of conveyor breakdown is negligible. Should you use preventative maintenance, or would it be cheaper to repair the conveyor only after it breaks down?

Number of breakdowns $012345$

Frequency of occurrence $0\mathrm{.}050\mathrm{.}100\mathrm{.}100\mathrm{.}100\mathrm{.}250\mathrm{.}40$

Please provide the support data for the decision. Also include some table to explain.