ECON 100A Lecture Notes - Lecture 16: Lagrange Multiplier
Document Summary
Problem set 3: f (x1, x2) find x1*, x2* s. t. f (x1, x2) is as high as it can be subject to x1* + x2* = x1x2 + (2 x1 x2: o. c. x2 - = 0. 2 x1 x2 = 0 x1 + x2 = 2. 1 & 2 x1 = x2 x2 / x1 = 1. 3 s. t. p1x1 + p2x2 = i when p1 = 5, p2 = 25, i = 100. P1x1 + p2 * 3p1 / p2 * x1 = i. X1* (p1, p2, i) = i / 4p1 p1 (i / 4p1) + p2x2 = i. X2* (p1, p2, i) = 3i / 4p2: a: cost is ax2. B: cost is by2 if we ship (x, y), tc = ax2 + by2 min x, y ax2 + by2 s. t. x+y = q. = ax2 + by2 + (q x y: 2ax = , 2by = , / 2.
