Find the minimum value of the function f($t?, y) = 2:2 + y2 subject to the constraint my = 16. Find the minimum value of the function f(:13, y) = 2:2 + 911,12 subject to the constraint my = 2. Find the absolute extreme values of f(:t':, y, z) = a: + 4y + 82 subject to :32 + y2 + 2:2 = 16. 1. Absolute minimum of f(:', y, z) is' ' 2. Absolute maximum of f($, y, 2:) is ' I 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, a: and 3; produced at each factory, respectively, and is expressed by the joint cost function: C(m, y) = 1:2?2 + my + 4y2 + 400 A) If the company's objective is to produce 1,800 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: I at Factory X and I at Factory Y B) For this combination of units, their minimal costs will be dollars. (Do not enter any commas in your answer.)