A company has the production function P(x, y), which gives the number of units that can be produced for given values of x and y; the cost function C(x, y) gives the cost of production for given values of x and y.

(a) If the company wishes to maximize production at a cost of $50,000, what is the objective function f? What is the constraint equation? What is the meaning of λ in this situation?
(b) If instead the company wishes to minimize the costs at a fixed production level of 2000 units, what is the objective function f? What is the constraint equation? What is the meaning of λ in this situation?