The production function of a competitive firm is described by the equation \(y = 8x_{1}^{1/2}x_{2}^{1/2}\) The factor prices are p1 = $1 and p2 = $4 and the firm can hire as much of either factor it wants at these prices.
a) What are the firm's cost minimizing levels of each input to produce y units of output?
b) Find the Cost function and the Marginal Cost function of the firm.