Problem $2(12$ points$)$:

Determine the optimum preventive maintenance frequency for each of the pieces of equipment if breakdown time is normally distributed:

Note: Round "Probability Ratio" to $\backslash (\backslash$mathbf$\{4\}\backslash )$ decimal places, and all other answers to $2$ decimal places. Negative values should be indicated by a minus sign.

$\backslash$begin$\{$tabular$\}\{$lll$\}$

& $\backslash$begin$\{$tabular$\}\{$l$\}$

Average Time $($days$)$ between $\backslash \backslash$

Breakdowns

$\backslash$end$\{$tabular$\}$ & $\backslash \backslash$

Equipment & $20$ & $2\backslash \backslash$

A$201$ & $30$ & $3\backslash \backslash$

B$400$ & $40$ & $4\backslash \backslash$

C$850$ & &

$\backslash$end$\{$tabular$\}$

$\backslash$begin$\{$tabular$\}\{$lll$\}$

& & $\backslash \backslash$

Equipment & Preventive Maintenance cost & Breakdown Cost $\backslash \backslash$

A$201$ & $\backslash (\backslash$$ $300\backslash )$ & $\backslash (\backslash$$ $2,300\backslash )\backslash \backslash$

B$400$ & $\backslash (\backslash$$ $200\backslash )$ & $\backslash (\backslash$$ $3,500\backslash )\backslash \backslash$

C$850$ & $\backslash (\backslash$$ $530\backslash )$ & $\backslash (\backslash$$ $4,800\backslash )$

$\backslash$end$\{$tabular$\}$

$\backslash$begin$\{$tabular$\}\{|$l$|$l$|$l$|$l$|\}$

$\backslash$hline Equipment & Probability Ratio & z & Interval $($days$)\backslash \backslash$

$\backslash$hline A$201$ & & & $\backslash \backslash$

$\backslash$hline B$400$ & & & $\backslash \backslash$

$\backslash$hline C$850$ & & & $\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$