Question

1. which corner point on this graph will result in the maximum value of the function $p = 3x - y$? graph view image description options: $(8, -4)$, $(14, -4)$, $(2, 8)$, $(14, 8)$

Explanation:

Step1: Identify Corner Points

The corner points from the options are \((8, -4)\), \((14, -4)\), \((2, 8)\), and \((14, 8)\).

Step2: Substitute into \(P = 3x - y\)

• For \((8, -4)\): \(P = 3(8) - (-4) = 24 + 4 = 28\)
• For \((14, -4)\): \(P = 3(14) - (-4) = 42 + 4 = 46\)
• For \((2, 8)\): \(P = 3(2) - 8 = 6 - 8 = -2\)
• For \((14, 8)\): \(P = 3(14) - 8 = 42 - 8 = 34\)

Step3: Compare Values

Compare the calculated \(P\) values: \(28\), \(46\), \(-2\), \(34\). The largest is \(46\) from \((14, -4)\).

Answer:

B. \((14, -4)\) (assuming the options are labeled A, B, C, D with \((14, -4)\) as option B; adjust label if needed)