MATH 125 Quiz: MATH 125 UWashington Quiz125Sp12 ans

• School: UW
• Department: Mathematics
• Course: MATH 125
• Professor: All

Document Summary

Mathematical economics final, december 6, 2016: consider the di erential equation y + 9y = 0. Then nd the solution that obeys y(0) = 1, y(0) = 2. Answer: the characteristic equation is 2 + 9 = 0. In such a case, the general real-valued solution is y(t) = cos 3t + sin 3t. Y(0) = 2 is y(t) = cos 3t + (3/2) sin 3t: minimize the function u(x, y) = (x 1)2 + (y 2)2 subject to the constraint x + 3y 3. Don"t forget to check the second-order conditions and constraint quali cation. Answer: since the constraint is linear, constraint quali cation is satis ed. The hessian of u is h = (cid:18) 2. 2(cid:19), which is positive de nite. solution to the rst-order conditions will be a local minimum. The lagrangian is l = (x 1)2 + (y 2)2 + (x + 3y 3).