20.10 (0) A firm has two variable factors and a production function, (x1,12) = 12 . The price of its output is 4. Factor 1 receives a wage of w, and factor 2 receives a wage of w/2. (a) Write an equation that says that the value of the marginal product. of factor 1 is equal to the wage of factor 1 and an equation that says that the value of the marginal product of factor 2 is equal to the wage of factor 2. Solve two equations in the two unknowns, 2, and x2, to give the amounts of factors 1 and 2 that maximize the firm's profits as a function of wj and w2. This gives $1 = and *2 = (Hint: You could use the first equation to solve for a, as a function of 12 and of the factor wages. Then substitute the answer into the second equation and solve for 12 as a function of the two wage rates. Finally use your solution for *2 to find the solution for $1.) (b) If the wage of factor 1 is 2, and the wage of factor 2 is 1, how many units of factor I will the firm demand? 0. How many units of factor 2 will it demand? How much output will it produce? How much profit will it make