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Find the vertex of the feasible region at which the constraint lines x + y = 40 and 2x + y = 60…

The vertex is \((20,20)\). Subtracting \(x+y=40\) from \(2x+y=60\) gives \(x=20\), and substituting back gives \(y=20\), which satisfies \(x\ge0\) and \(y\ge0\). The…

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Find the vertex of the feasible region at which the constraint lines x + y = 40 and 2x + y = 60 intersect for the given L.P. (Linear Programming),
Maximize Z = 8x + y
Constraints are x + y ≤ 40
2x + y ≤ 60
x ≥ 0, y ≥ 0

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Answer and explanation

Correct answer A

The vertex is (20,20)(20,20). Subtracting x+y=40x+y=40 from 2x+y=602x+y=60 gives x=20x=20, and substituting back gives y=20y=20, which satisfies x≥0x\ge0 and y≥0y\ge0. The vertices (0,40)(0,40) and (30,0)(30,0) lie where each of these lines meets an axis, and (40,60)(40,60) lies outside the feasible region.

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