Ejercicio de pearson, Ejercicios de Análisis Económico

¡Descarga Ejercicio de pearson y más Ejercicios en PDF de Análisis Económico solo en Docsity!

20/9/22, 12:52 Actividad 1 - Guía 4-Laura Cortes Instructor: JOSE ALEXANDER Student: Laura Cortes FUENTES MONTOYA Date: 09/20/22 Course: Análisis Multivariado y Funcional G1C3 Assignment: Actividad 1 - Guía 4 Find the points on the ellipse e + 5 = 1 where f(x,y) = xy has its extreme values. First find the values of x, y, and A for which Vf=/Vg and g(x,y) = 0. The gradient of fis given below. Ví=yi+xj Find the gradient of g(x,y) = e + 5 -1=0. AVg=224xi+ 104yj Therefore, any points that are extreme values of f(x,y) = xy, given the constraint e + sy - 1=0, must satisfy the equation yi + xj=22xi+ 104yj. Thus, the coordinates of any such extreme values must satisfy the scalar equations y = 2Ax and x=10%y. Now substitute the expression for x into the expression for y and solve for A. y = 2x 2M101y) 20M y Note that one solution to this equation is y = 0, in which case x=0 as well. However, the point (0,0) is not on the ellipse, so y*0. Now solve for cases in which y % 0. y = 202y 4 an * Divide both sides by 20y. 1 it+=-=h Take the square root of both sides. 24/5 Next, substitute the value of A and solve for x. x= 104y 4 10| += 5) 5 = ty Eh Now substitute the expression for x into the original equation and solve for y. boy =1 2 5 EN 5 Simplify. sy + sy https://xlitemprod.pearsoncmg.com/api/v1/print/highered 112