A company produces x units of type A and y units of type B of a good. The maximal quantities that the company can produce weekly are given by 2x2 + y2 = b for a positive constant b. The profits are $4 per unit of type A and $2 per unit of type B. (a) Find x and y such that the profit is maximized. (b) Assuming that currently b = 12 and that there is a possibility to increase b to 27 at a cost of 5. Is it worth to do it