The ${0\mathrm{.}25}^{\text{'}\text{'}}$ thick bar shown below is made of cast iron. It is fixed at its left end and subjected to a load of $1200$ lbf at its right end. $(60$ Points$)$

a$.$ By hand calculation, determine the max stress in the $x-$direction at the hole. Write the answer below and include your work on subsequent pages.

b$.$ By hand calculation, determine the max stress in the $x-$direction at the fillets. Write the answer below and include your work on subsequent pages.