Question

question 5 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 and shaded regions, with a red vertical line at x=6, a blue line from (0,15) to (15,0), and shaded areas.
a. (6, -2)
b. (8, 9)
c. (12, 4)
d. (2, 12)

Explanation:

Step1: Analyze constraints

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

Step2: Check option A \((6, - 2)\)

\(y=-2\) is negative, but weight can't be negative. So this is not viable.

Step3: Check option B \((8,9)\)

\(x = 8\), but \(x\leq6\) is a constraint. \(8>6\), so this is not viable.

Step4: Check option C \((12,4)\)

\(x = 12\), and \(12>6\), which violates the \(x\leq6\) constraint. Not viable.

Step5: Check option D \((2,12)\)

• Check \(x\leq6\): \(2\leq6\), satisfies.
• Check \(x + y\leq15\): \(2 + 12=14\leq15\), satisfies.
• \(x = 2\geq0\), \(y = 12\geq0\), satisfies non - negative constraints.

Answer:

D. \((2, 12)\)