Evaluate the line integral, where c is the given curve. (x + 6y) dx + x2 dy, c c consists of line segments from (0, 0) to (6, 1) and from (6, 1) to (7, 0)

Split into two component segments, and , parameterized by

respectively, with , where .

We have

where

so the line integral becomes

answer: evaluate the objective function at each vertex to determine which - and -values, if any, maximize or minimize the function. example: find the minimum value and maximum value of the objective function f ( x , y ) = 4 x + 5 y , subject to the following constraints