Question

question 6 of 10
a basket holds at most 15 pounds of apples and oranges. there are no more than 6 pounds of apples in the basket. this graph shows the system that represents this scenario, where x is the weight of the apples and y is the weight of the oranges.
which point represents a viable solution?
graph: x-axis (apples, pounds) from 0 to 16, y-axis (oranges, pounds) from 0 to 16. a line from (0,15) to (15,0), a vertical line at x=6, and shaded regions. text description for graph

Explanation:

To determine the viable solution, we analyze the constraints:

1. The total weight of apples (\(x\)) and oranges (\(y\)) must satisfy \(x + y \leq 15\) (since the basket holds at most 15 pounds).
2. The weight of apples must satisfy \(x \leq 6\) (no more than 6 pounds of apples).
3. Both \(x \geq 0\) and \(y \geq 0\) (weights cannot be negative).

A viable solution must lie in the overlapping region of these inequalities (the purple-shaded area, since it satisfies \(x \leq 6\) and \(x + y \leq 15\) with \(x, y \geq 0\)). For example, the point \((4, 10)\):

• Check \(x \leq 6\): \(4 \leq 6\) (true).
• Check \(x + y \leq 15\): \(4 + 10 = 14 \leq 15\) (true).
• Check \(x, y \geq 0\): \(4 \geq 0\) and \(10 \geq 0\) (true).

Other points in the purple region (e.g., \((2, 12)\), \((5, 9)\)) would also work, but \((4, 10)\) is a clear example of a viable solution.

Answer:

A point like \(\boldsymbol{(4, 10)}\) (or any point in the purple-shaded region where \(x \leq 6\), \(y \geq 0\), and \(x + y \leq 15\)).