Suppose the joint cost function of a firm producing two products X and Y is given by C = 250X2 + 120Y2 . Assuming that output of the two products is restricted at 1369. Using Lagrangian multiplier technique find the amounts of X and Y that will minimize cost and compute this cost. Also examine the cost implications of changing this optimal combination so as to produce 236 additional units of X and 236 fewer units of Y.