In Fig. H.5, two somewhat odd cases could occur. The solution could be at d, but the contour of the objective function could be (a) tangent to the b1 constraint, or (b) tangent to the b2 constraint,...

In Fig. H.5, two somewhat odd cases could occur. The solution could be at d, but the contour of the objective function could be (a) tangent to the b1 constraint, or (b) tangent to the b2 constraint, at that point. What happens to the conditions [H.27]–[H.30] in such a case? [Hint: consider what happens in case (a) if the b2 constraint shifts outward and inward, and in case (b) if the b1 shifts. What can be said about the relevant Lagrange multiplier in each case?]