The feasible region for a linear programming problem is defined by x >= 0, y >= 0, 2x + 3y <= 6, and x + 4y <= 4. What is the maximum value of Z = 2x + 3y?

A. 6 — The vertices of the feasible region are (0,0), (3,0), (0,1), and the intersection of the lines. Evaluating Z at these points, the maximum value is 6 at (3,0).

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$The feasible region for a linear programming problem is defined by x \geq 0, y \geq 0, 2 x + 3 y \leq 6, and x + 4 y \leq 4 . What is the maximum value of Z = 2 x + 3 y ?$

A. $6$
B. $4$
C. $3$
D. $5$

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Correct answer: A — $6$

Solution

The vertices of the feasible region are (0, 0), (3, 0), and (0, 1) . Evaluating Z = 2 x + 3 y at these points gives 0, 6, and 3 respectively. The maximum value is 6 .

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The feasible region for a linear programming problem is defined by x≥0, y≥0, 2x+3y≤6, and x+4y≤4. What is the maximum value of Z=2x+3y?

Solution

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More Linear Programming practice questions

$The feasible region for a linear programming problem is defined by x \geq 0, y \geq 0, 2 x + 3 y \leq 6, and x + 4 y \leq 4 . What is the maximum value of Z = 2 x + 3 y ?$