A firm produces two goods: widgets (X) and woozles (Y). Its profit function is given by: Π = 55X – 2X2 – XY – 3Y2 + 100Y and its maximum output capacity is X + Y = 17. (a) Use the Lagrangian method to calculate the output mix the firm should produce. (b) Estimate the effects on profits if output capacity is expanded by 1 unit. (c) You are hired by the firm to evaluate a proposal from its Engineering Department that the firm’s output capacity be expanded to 33. Do you agree with the proposal? If not, what output capacity would you recommend?