Solve the following binary LPP and write$/$type the optimum value of the objective function and optimum values of all $p$

Max,$P_1+4\mathrm{.}8P_2+6P_3+6\mathrm{.}8P_4+6\mathrm{.}6P_5+4\mathrm{.}9P_6$

s$.$t$.,20P_1+55P_2+47P_3+38P_4+90P_5+63P_{6}175$

$15P_1+45P_2+50P_3+40P_4+70P_5+70P_{6}150$

$P_4-P_6=0$

$P_1-P_{2}0$

$P_3+P_{5}1$

$P_1+P_2+P_3+P_4+P_5+P_{6}3$

$P_i=0or1$