Question

F(x,y)=3x−6y over the triangle with vertices (0, 0), (6, 0), and (0, 7).

Options:
a) Maximum: 18, Minimum: -42
b) Maximum: 12, Minimum: -36
c) Maximum: 24, Minimum: -30
d) Maximum: 15, Minimum: -48

Answer 1

The maximum and minimum values of the function f(x, y) = 3x - 6y over a given triangle with vertices (0, 0), (6, 0), and (0, 7) are 18 and -42 respectively.

Step-by-step explanation:

The question is asking us to find the maximum and minimum values of the function f(x, y) = 3x - 6y over a given triangle with vertices (0, 0), (6, 0), and (0, 7).

To find the maximum and minimum values, we need to evaluate the function at the vertices of the triangle.

Plugging in the coordinates of the vertices into the function, we get f(0, 0) = 0, f(6, 0) = 18, and f(0, 7) = -42. Therefore, the answer is Option a) Maximum: 18, Minimum: -42.