Problem $4(20$ Points$)$

A machine part with an endurance limit of $45$ kpsi and an ultimate strength of $80$ kpsi is cycled $10$ percent of the time at $71$ kpsi $,40$ percent at $57$ kpsi $,$ and $50$ percent at $53$ kpsi $.$ Let $\backslash ($ f$=0\mathrm{.}9\backslash )$ and based on Miner's method estimate the number of cycles to failure.