Exam Maths II, Ejercicios de Matemática Financiera

¡Descarga Exam Maths II y más Ejercicios en PDF de Matemática Financiera solo en Docsity!

MATEMATIQUES II. Curs 2017-18 Códi Assignatura 102344. Exámen Parcial 09-04-2018 1. Consider the following problem to optimize f(x, y) = y + 2x2 subject to S =4f(2,y) ER y > 1, y+2<2y-—x<2) (a) (2 pt) Draw the set S. Determine whether the set S is open, closed, bounded, compact, and/or convex. Do not foget to justify your answer. (b) (1.5 pt) Draw the contour map for the function f(x, y). (c) (1.5 pt) Using level curves find the maximums and minimums for f on $. (d) (1 pt) What is the absolute minimum of f(x, y) on 57. 2. Given the system of equations: t=zy+az = 4 tI+ayoz = -—1 T+y+az = 2 (a) (1 pt) Let A be the matrix of coefficients and B the column matrix of constants. Compute the determinant of A. (b) (1 pt) For which values of the parameter a is the matrix A not invertible ? (c) (1 pt) For the values found in the previous question give the general solution for the system, if any exists. (d) (1 pt) Solve the system, if possile, for a = 1. Remember: ALL ANSWERS HAVE TO BE DULLY JUSTIFIED!