Acme Inc, using the input of labor (y1

Acme IIIC, using the input of labor (yl O) to produce widgets 0) and smidgets (Y3 0). Production is given by G(yl) = (yl), where 4-3!/3 G. You can think of G as the total amount of parts produced and those can be assembled into widgets and smidgets. (a) Write the Lagrangian for the profit-maximization problem. (b) Solve for the profit-maximizing supply. Think carefully; there are 3 cases to consider and you can ignore the zero-measure "edge" case