Use the method of Lagrange multipliers to solve optimization problems with two constraints. A firm manufactures a commodity at two different factories, Factory X and Factory Y. The total cost (in dollars) of manufacturing depends on the quantities, :13 and y produced at each factory, respectively, and is expressed by the joint cost function: C(m, y) : 1m2 | my | 4/92 | 400 A) If the company's objective is to produce 800 units per month while minimizing the total monthly cost of production, how many units should be produced at each factory? (Round your answer to whole units, i.e. no decimal places.) To minimize costs, the company should produce: at Factory X and at Factory Y B) For this combination of units, their minimal costs will be commas in your answer.)