a)Given that Q = 2000k L , C = R12000, W = 60 and r = 40.Determine the quantity of Labour and Capital that the firm should use in order to maximize output.What is this level of output?

b)Suppose the utility function Tracey is givenU = f(X₁, X₂) = X₁^0.25X₂^0.75. Given that the price of commodity X₁is Kshs.10 per unit and that of community X₂is Kshs.15 per unit. Using Lagrangian multiplier technique determine units of the two commodities Tracey will buy given an income of R30,000 in order to maximize her utility