Chapter 10.9, Problem 23E

To determine

To find: the coordinates of all the vertices and determine whether the solution set bounds or not

Answer to Problem 23E

The solution is bounded.

Explanation of Solution

Given:

  $y<\frac{1}{4}x+2$

  $y\ge 2x-5$

Calculation:

Consider the following inequalities:

  $y<\frac{1}{4}x+2$

  $y\ge 2x-5$

Step (1):

Graph the equation corresponding to the first inequality using dotted line. Shade the region that satisfies the inequality.

  

Step (2):

Graph the second equation corresponding to the inequality using solid line on the same sheet.

Shade the region that satisfies the inequality and also identify the common region satisfying both the inequalities.

  

The region shaded in blue and purple satisfies the second inequality.

Thus, the purple color shaded region is the solution of the system of two inequalities. Hence the solution is bounded.

Conclusion:

Therefore, the solution is bounded.