Solve plz with work

6. A factory produces noodles. The quantity of noodles Q {measured in kilograms) that they produce in a day can be expressed as a function of the number of hours L that it uses on labour, and the amount of capital K that it uses by the formula LK2 20 . The employees are paid 12$ per hour, and each unit of capital costs 30$. Q(L,K) = (a) (10 points) The factory has just received a large order from a chain of restaurants of 400 kg of noodles. How many hours of labour and how many units of capital should the factory use in order to minimize their costs? Use the method of Lagrange multipliers. Don't forget to check that the solution you nd is indeed a minimum