Question 1 (1) The short-run production function of a firm is given as q- f(L,K) while the cost constraint is given as C-WL+ K, where q is output, L is labour, Kis capital, wis reward to labour, ris reward to capital Using the Lagrangian method, prove that cost minimization subject to a production constraint will yield equivalent result as output maximization subject to a cost constraint (10 marks) 0.75 02 (ii) A consumer utility function is given as U(X,Y)= 10 X's y , where X represents clothing and Y represents shoes. If her income is $960, the price of clothing is $48, and the price of shoes is $32, calculate the consumer utility maximizing bundle (XY) using the Lagrangian method. (10 marks)