Question

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? a. (6, -2) b. (2, 12) c. (12, 4) d. (8, 9)

Explanation:

Step1: Analyze constraints

The constraints are: \( x + y \leq 15 \) (total weight at most 15), \( x \leq 6 \) (apples at most 6), and \( x \geq 0, y \geq 0 \) (weights non - negative).

Step2: Check option A

For point \( A=(6, - 2) \), \( y=-2\) which is negative. Since weight can't be negative, this is not viable.

Step3: Check option B

For point \( B=(2,12) \):

• Check \( x\leq6 \): \( 2\leq6 \), which is true.
• Check \( x + y\leq15 \): \( 2 + 12=14\leq15 \), which is true.
• \( x = 2\geq0 \) and \( y = 12\geq0 \). So this point satisfies all constraints.

Step4: Check option C

For point \( C=(12,4) \):

• Check \( x\leq6 \): \( 12>6 \), so this does not satisfy the constraint on the weight of apples.

Step5: Check option D

For point \( D=(8,9) \):

• Check \( x\leq6 \): \( 8>6 \), so this does not satisfy the constraint on the weight of apples.

Answer:

B. (2, 12)