Solve by hand

(1) Write the standard form of the following LPs and solve them using simplex algorithm and find out if LP has a unique optimal solution, multiple optimal solution or LP is unbounded. Show all the steps and write all the optimal solutions and optimal value if there is any. (each part 6 points) (a) maxs.t.z=x1+3x2x12x202x1+x245x1+3x215x1,x20 (b) maxs.t.z=2x1+2x2x1+x262x1+x213x1,x20 (c) maxs.t.z=x1+3x2x12x24x1+x23x1,x20