Find z*, s₁*, s₂*, y₁*, y₂*, e₁*, e₂*, e₃*, and w*.

Is x* optimal for the primal LP? (yeso)

Is y* optimal for the dual LP? (yeso)

Consider the following LP: maximize7x1+9x2+2x3subjectto2x1+3x2+7x35x1+x2+8x32x1,x2,x30 Use the complementary slackness theorem to check if x=(1,1,0) 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=(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, and let w be the value of the objective of its dual at y. Provide your answers by filling in the blanks below