(5) (14 pm) The revenue of a company is given by the function R(z,y, z) = a:(yz + 1), where z, y, 2: refers to the units of input in labour, capital and advertising. The manager of the company wants to maximize the revenue but maintaining an upper bound on the total cost, that is to : maximize R(:r, y, 2:) subject to a: + y2 + 22 <_: it: y o z write down the kuhntucker lagrangian and rst order conditions for this optimization problem. check that kuhn-tucker version ndcq is satised. explain why at any solution to constraint :1: y2 g binding. find maximizer of>