Find the absolute maximum and minimum values of the linear function f(x, y) = -2x + y - 10 on the polygon 0 $\le$ x $\le$2, 0 $\le$ y $\le$ 2, y - x $\le$ 1.
A) maximum -9, minimum -14
B) maximum -9, minimum -12
C) maximum -8, minimum -12
D) maximum -8, minimum -15
E) maximum -9, minimum -10

Question

Quizplus · Accepted Answer

The absolute maximum and minimum values of a linear function on a polygon can be found by evaluating the function at the vertices of the polygon. The vertices of the given polygon are (0,0), (0,1), (1,2), and (2,1). Evaluating f(x, y) at these points gives: f(0,0) = -10, f(0,1) = -9, f(1,2) = -10, and f(2,1) = -14. Therefore, the maximum value is -9 and the minimum value is -14.

Find the Absolute Maximum and Minimum Values of the Linear ≤\le≤

Find the Absolute Maximum and Minimum Values of the Linear $\le$