Consider the following LP: maximize 7x1 + 92 + 2x3 subject to 2x1 +3x2+7x3 < 5 x1 + x2 + 83 2 x1, x2, x3 0 Use the complementary slackness theorem to check if x*=(2, 0, 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*=(S1*,S2*) denote the values of the slack variables of the above LP corresponding to x=x*, and let Let e*=(e*,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*= S1 = S2 = Y1* = Y2* = e1' e2 e3' W*= Is x* optimal for the primal LP? (yes/no) Is y* optimal for the dual LP? (yes/no)