Question

Which of the following ordered pairs is in the feasible region for the following system of inequalities? 8x-y>9 (1)/(2)x+6>=y y+1>(-1)/(3)(x-9)

Answer 1

To find the feasible region for the given system of inequalities, plot each inequality separately and shade the regions that satisfy the inequalities. The feasible region is where all the shaded regions intersect. In this case, the only ordered pair in the feasible region is (3, 8).

Step-by-step explanation:

To find the feasible region for the given system of inequalities, we need to graph each inequality separately and then find the region where all the graphs intersect.

Graphing the first inequality, 8x-y>9, we can start by plotting the line y=8x-9. Since the inequality is greater than, the region above the line is the feasible region.

Now let's graph the second inequality, (1)/(2)x+6>=y. We can rewrite it as y<=(1)/(2)x+6. Plotting the line y=(1)/(2)x+6, we can shade the region below the line since the inequality is less than or equal to.

Next, we graph the third inequality, y+1>(-1)/(3)(x-9). Rewriting it as y>(-1)/(3)(x-9)-1, we can plot the line y=(-1)/(3)(x-9)-1 and shade the region above the line because the inequality is greater than.

The feasible region is the region where all three shaded regions intersect. In this case, we can see that the only ordered pair that lies in the feasible region is (3, 8).

Answer 2

To determine which of the given ordered pairs is in the feasible region, substitute the values into the inequalities and check for satisfaction. The feasible region is the set of ordered pairs that satisfy all three inequalities.

Step-by-step explanation:

To determine which of the given ordered pairs is in the feasible region for the system of inequalities, we need to substitute the x and y values of each pair into the inequalities and check if they satisfy the inequalities.

For example, let's take the ordered pair (2, 5). Substituting these values into the first inequality, we get 8(2) - 5 > 9, which simplifies to 11 > 9. This statement is true, so (2, 5) satisfies the first inequality. Similarly, we can substitute the values into the other two inequalities to check their satisfaction.

After checking all the ordered pairs, the feasible region is the set of ordered pairs that satisfy all three inequalities.