In example 3.77 Robinson the producer makes a profit of wh* + pq*. This is Robinson the

Question:

In example 3.77 Robinson the producer makes a profit of wh* + pq*. This is Robinson the consumer's income, so his budget set is
X = {(h,q : wh + pq ≤ wh* + pq*}
This is half space below the separating hyperplane in figure 3.17. Note that A⊆X.
(h*, q*) is the optimal choice in the feasible set A. Show that it is also Robinson the consumer's optimal choice in the larger budget set X. Consequently (h*,q*) solves the consumer's problem when the prices are w and p.