Question

This graph shows the inequality 25x+15y≥200, which represents the number of chairs and tables a carpenter can build, where x represents the number of chairs and y represents the number of tables. Which labeled points on the graph indicate a viable combination of chairs and tables that meets the carpenter's production goal?
(5, 2)
(5, 2)

None of the points are a viable solution
None of the points are a viable solution

(15, 4.5)
(15, 4.5)

(18, 10)
(18, 10)

Answer 1

To determine which labeled points represent viable combinations that meet the inequality \( 25x + 15y \geq 200 \), we can start by checking each point against the inequality.

1. **Point (5, 2)**:
\[
25(5) + 15(2) = 125 + 30 = 155
\]
Since \( 155 < 200 \), this point does NOT meet the production goal.

2. **Point (15, 4.5)**:
\[
25(15) + 15(4.5) = 375 + 67.5 = 442.5
\]
Since \( 442.5 \geq 200 \), this point DOES meet the production goal.

3. **Point (18, 10)**:
\[
25(18) + 15(10) = 450 + 150 = 600
\]
Since \( 600 \geq 200 \), this point DOES meet the production goal.

In summary:
- (5, 2) is NOT a viable solution.
- (15, 4.5) IS a viable solution.
- (18, 10) IS a viable solution.

So the viable combinations of chairs and tables that meet the carpenter's production goal are (15, 4.5) and (18, 10).