can you show me how to work backwards in determining the optimal PM expense?

The manager of Cheryl's hospital is determining how often to perform preventive maintenance. When the testing machine fails, it costs the company $15,000 in lost production. However, the cost of preventive maintenance is somewhat expensive. The cost of performing preventive maintenance is $3,000.

Weeks between Preventive Maintenance	Average Number of Breakdowns between Preventive Maintenance
1	0.039
2	0.110
3	0.131
4	0.151
5	0.176

a) Which interval (weeks between preventive maintenance) do you recommend for performing preventive maintenance? Base this recommendation on the economics as presented.

PM 1 per week: 3,000 + (15,000 x 0.039) = 3,000 + 585 = $3,585

PM every 2 weeks: (3,000 +(15,000 x 0.11)) / 2 = 4,650 / 2 = $2,325

PM every 3 weeks: (3,000 +(15,000 x 0.131)) / 3 = 4,965 / 3 = $1,655

PM every 4 weeks: (3,000 +(15,000 x 0.151)) / 4 = 5,265 / 4 = $1,316.25

PM every 5 weeks: (3,000 +(15,000 x 0.176)) / 5 = 5,640 / 5 = $1,128

With the preventative maintenance being so high and the chance of failure only slightly increasing, it is most cost effective to perform PM every 5 weeks with the expense estimated at $1,128

b) Suppose that the company has outsourced the preventive maintenance work. The cost of the preventive maintenance work is negotiable.With everything else being the same as provided above, what is the preventive maintenance cost that makes the manager indifferent between a two-week and a three-week preventive maintenance strategy? Assume that the preventive maintenance costs the same regardless of the weeks between preventive maintenance.