Consider the following LP: maximize 3x1 + 6x2 +10x3 subject to 3x1 + x2 + I3 < 2 5x1 + 22 + 2x3 3 x1, x2, x3 0 Use the complementary slackness theorem to check if x*=(0, 2, 0) is an optimal solution of this LP. Assuming x* is indeed an optimal solution, compute the corresponding dual optimal solution y*. Then make a conclusion on whether the assumption is correct. Let s*=($1*,52*) denote the values of the slack variables of the above LP corresponding to x=x*, and let Let e*=(e1*,e2*, e3*) denote the values of the excess variables of its dual LP corresponding to y=y*. Let z* be the value of the objective of the LP above at x*, and let w* be the value of the objective of its dual at y*. Provide your answers by filling in the blanks below. z*= 51" = S2* Y1*= Y2* = e* = e2* e3* W*= Is x* optimal for the primal LP? (yes/no) Is y* optimal for the dual LP? (yes/no)