3.1.4 Linear Programming - Practice
1. Graph the feasible region for the given constraints.
2. Maximize the objective function P = 5 x + 7 y for the given constraints.
x ≥ 0 y ≥ 0
x ≥ 0 y ≥ 0
2 x + 3 y ≤ 1500 3 x + 2 y ≤ 1500
2 x + 3 y ≤ 18 5 x + 2 y ≤ 23
3. Maximize the objective function P = 5 x + 3 y for the given constraints.
4. A furniture company has 400 board ft of teak wood and can sustain up to 450 hours of labor each week. Each chair produced requires 5 ft of wood and 10 hours of labor, and each table requires 20 ft of wood and 15 hours of labor. If a chair yields a profit of $45 and a table yields a profit of $80, what are the numbers of chairs and tables that should be produced each week in order to maximize the company’s profit?
x ≥ 0 y ≥ 0
3 x + 6 y ≤ 48 2 x + 8 y ≤ 56
174
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