Maximize the objective function P = 4x + 3y subject to the constraints x ≤ 5, x + y ≤ 6, y ≤ 4, x ≥ 0, y ≥ 0.

May 7, 2026Mathematics

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5 stepsMay 7, 2026

Answer

4x + 3y$ subject to the constraints:

Step 1: Maximise the objective function $P = 4x + 3y$ subject to the constraints:

$x \le 5$
$x + y \le 6$
$y \le 4$
$x \ge 0$ (implied for typical linear programming problems)
$y \ge 0$ (implied for typical linear programming problems)

Step 2: Identify the vertices of the feasible region. The feasible region is bounded by the lines $x=0, y=0, x=5, y=4, x+y=6$ . The vertices are the intersection points of these boundary lines that satisfy all constraints:

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Maximise the objective function P = 4x + 3y subject to the constraints: 1. x 5 2.

Asked on May 7, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on May 7, 2026

Step 1: Maximise the objective function P = 4x + 3y subject to the constraints: 1. x 5 2. x + y 6 3. y 4 4. x 0 (implied for typical linear programming problems) 5. y 0 (implied for typical linear programming problems) Step 2: Identify the vertices of the feasible region. The feasible region is bounded by the lines x=0, y=0, x=5, y=4, x+y=6. The vertices are the intersection points of these boundary lines that satisfy all constraints: