MATH 125 Quiz: MATH 125 UWashington Quiz125A13 ans

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

Document Summary

At most two of the constraints can bind. Since all rows are non-zero and any two rows are independent, the rank will equal the number of binding constraints. Ndcq is satis ed: find the solution to the maximization problem. Answer: the lagrangian is l = x +py 0(px + y 10) + 1x + 2y. Equation (1) tells us p 0 = 1 + 1 1. Then 0 > 0 and it follows that px + y = 10 by complementary slackness. There are now three cases to consider: 1) x = 0, y = 10; 2) x = 10/p, y = 0; 3) x, y > 0. In case (1), 2 = 0 by complementary slackness, so 0 = 1/2 10. This requires p/2 10 1, that is, p2 40. In case (2), equation (2) is violated due to division by zero. In case (3), 1 = 2 = 0 by complementary slackness.