3. nonlinear shadow price Return to our discussion of shadow prices, and the maximization in

(8.2). Now suppose the criterion function is ω(x, y) = 10x2 + 12y2.

Determine an optimal solution, along with the shadow prices on the two constraints. Repeat for the case where the first constraint is x+y ≤ 9. Is the gain from relaxing the constraint numerically equal to the original shadow price multiplied by the one unit increase in the constraint? Explain.