1. Consider the following constrained optimization problem: you have to decide about purchasing , and x2 units of goods with prices p, p2 (per unit). Utility of these goods in the production (output) is described by the utility function: 1-a u(x, x) = axix 1/2 - where a (0, 1) and a > 0 is a given constant. 2 You are given the fixed utility U that must be achieved by the purchased amounts (i.e. u(x, x) = U) while the total cost px + p2x2 is minimized. a) Formulate the optimization problem to be solved. [2] b) Find the solution of the problem. [5] c) How will the optimal cost of the purchase change if the total utility U is de- creased by 2%. [3]