Chapter 11.7, Problem 56AYU

To determine

To write: A system of linear inequalities for the given graph.

Answer to Problem 56AYU

Solution:

$x \ge 0, y \ge 0, x \le 5, y \le 6, - 2x + y \le 2, 3x + 4y \ge 12$

Explanation of Solution

Formula Used:

Equation of a line is $y = mx + b$.

Where $m = slope = \frac{y_2 - y_1}{x_2 - x_1}$ (if two points $\left(x_1, y_1\right), \left(x_2, y_2\right)$ are given.)

$b = y - intercept$

Given:

Graph with feasible points.

Calculation:

From the graph, it can be see that

$x \ge 0$

$y \ge 0$

$x \le 5$

$y \le 6$

To find an equation of a line passes through $\left(5, 2\right), \left(4, 0\right)$

From formula used,

$m = - 2/ - 1 = 2$

$b = 2$

$y = 2x + 2$

Therefore, $- 2x + y \le 2$ (from the graph).

To find an equation of a line passes through $\left(0, 3\right),\left(4, 0\right)$.

From formula used,

$m = - 3/4$

$b = 3$

$y = - \left(3/4\right)x + 3$

Therefore, $3x + 4y \ge 12$ (from the graph).