A firm uses two inputs to produce its output via the Cobb-Douglas production function z = x^a y^b, where a = b = .5. Its current level of inputs is x = 25 y = 100. The firm will introduce a new technology that will change the b-exponent on its production function to b = .504, with no change to a. Use calculus to estimate the input combination which will keep the total output the same and the sum of the inputs the same. (Hint: Work with the system x^a y^b = c (or better a ln x + bln y = ln c) and x+y = 125