Carmela's pasta factory employs workers and pasta machines according to the following production function f(L, K) = L^1/2K^1/2 . The hourly cost of capital is £10 and the hourly cost of workers is £40. Write out the Lagrangian for the cost-minimization problem. Suppose Carmela wishes to produce 1000 units of pasta. How much labour and capital should she employ? How much will it cost to produce 1000 units? An order arrives doubling the amount of pasta Carmela needs to produce. Assuming she is unable to purchase more capital, how much will it cost to meet the new production level?