Suppose a refinery must ship finished goods to some storage tanks using two pipelines, A and B. The cost of shipping units on A is ^2; the cost of shipping units on B is ^2, where >0 and >0 are given. How can one ship units while minimizing the cost? a) Write down the optimization problem in standard form. b) Formulate the first order optimality conditions. c) Find x, y and the minimum cost