A firm's production function for its product is given as follows: = (,) = 60 0.5 0.25 Where q = output; L is the quantity of labor employed, measured in man-hours, and whose cost per unit (wage rate) is $4 per hour; K is the quantity of capital employed, measured in machine-hours, and whose price per machine hour is $5. The total cost outlay, TC, allocated by the finance department is set at $150. REQUIRED:

a) Use the Lagrange multiplier method to determine the optimal amount of labor and capital that maximizes output. What is the maximum output? (10 Marks)

b) What does the second-order condition imply for the solution found in (a) above?