A $4$ MW$,0\mathrm{.}707$ industrial plant is supplied from a $6$ MVA three$-$phase power transformer. A $1\mathrm{.}0$ MW$,11$ kV$,0\mathrm{.}8$ leading power factor, $88\%$ efficient, $3-$phase synchronous motor is to be installed in the plant. Answer the following questions: $(8$ Marks$)($a$)$ What is the new overall power factor of the plant. $($b$)$ Is the $6$ MVA transformer over$-$loaded after connecting the synchronous motor. $($c$)$ If yes find the over$-$loading percentage