Problem 12.3 A firm operates 3 processes, which produce 3 goods and pollution (P) as a function of the levels of operation of the processes. The pollution level is given by P(X1,X2 X3) = 3x] + 3x} + 3x] + 2(x1x2 + xx3 + XzX3) where x/ 2 0 is the amount of good / produced. The firm faces strictly positive prices (pi > 0, 5 pz> 0, p)>0) for the outputs. It is regulated and not allowed to produce a higher pollution level than M. The firm wishes to maximize revenue (Epix) subject to the pollution constraint. By examining the Kuhn Tucker conditions, show that, at the optimum the pollution constraint is binding