A firm has a production technology given by:y=x^0.25z^0.5, where x is labour input, z is the amount of physical capital. Initial input prices are given by w =1 and r = 1. Suppose now that both capital and labour are variable inputs.

Assume that the price of physical capital was doubled and denote the product price byp, p>0.Then,determine the profit gained from profit-maximizingoutput y*, the "shut down" and zero profit conditions.

Full explanation please