4. A firm manufactures outputs y1 and y2 using two inputs x1 and x2. The production function is (y1,y2)=f(x1,x2)=(x11/2,x11/2x21/2). Let pi denote the unit price of yi, and wi that of xi. Describe the firm's optimization problem and derive the equations that define the critical points of the Lagrangean. Calculate then the solution when p1=p2=1 and w1=w2=2