Linear Programming

CBSE Class 12 Mathematics · 92 board questions from this chapter; 91 listed below, 2023–2026 · 1 of them repeated across years

• In the graph, the feasible region representing the Linear Programming Problem for maximising objective function Z=px+qy, p, q>0…2026
• The region represented by the system of inequations 3 x+y ≥ 3, 2 x-y ≥-5, x, y ≥ 0 is:2026
• The corner points of the feasible region determined by the system of linear constraints are (0, 0), (0, 40), (20, 40) (60, 20)…2026
• In a linear programming problem, the linear function which has to be maximized or minimized is called2026
• For the feasible region shown below, the non-trivial constraints of the linear programming problem are2026
• The feasible region of a linear programming problem with objective function Z=5 x+7 y is shown below: The maximum value of Z -…2026
• The degree of an objective function of a linear programming problem is2026
• Assertion: Consider a Linear Programming Problem with minimise Z=x+2 y subject to constraints 2 x+y ≥ 3, x+2 y ≥ 6, x, y ≥ 0…2026
• Solve the following linear programming problem graphically: Maximize Z=8000 x+12000 y Subject to constraints 3 x+4 y ≤ 60; x+3 y…2026
• Solve the following Linear Programming Problem graphically: Maximise Z=200 x+120 y subject to the constraints x+y ≤ 300; 3 x+y ≤…2026
• Solve the following Linear Programming Problem graphically: Maximize Z=20 x+10 y subject to constraints x+2 y ≤ 28; 3 x+y ≤ 24; x…2026
• Solve the following Linear Programming Problem graphically: Minimize Z=20 x+10 y subject to x+2 y ≤ 40; 3 x+y ≥ 30; 4 x+3 y ≥ 60;…2026
• Solve the following Linear Programming Problem graphically: Maximize Z=(2 x)/5+(3 y)/10 subject to constraints 2 x+y ≤ 1000; x+y…2026
• Solve the following linear programming problem graphically: Minimize Z=13x-15y Subject to constraints x+y ≤ 7; 2 x-3 y+6 ≥ 0; x ≥…2026
• Solve the following linear programming problem graphically: Maximize Z=10500 x+9000 y Subject to constraints x+y ≤ 50; 2 x+y ≤…2026
• Solve the following linear programming problem graphically: Maximize Z=4500 x+5000 y Subject to constraints x+y ≤ 250; 25 x+40 y…2026
• Solve the following Linear Programming Problem graphically: Maximise Z=600 x+400 y subject to the constraints x+2 y ≤ 12; 4 x+5 y…2026
• Solve the following Linear Programming Problem graphically: Maximize Z=8 x+8 y subject to the constraints x-20 ≤ 0; 2 x+3 y ≤…2026
• Solve the following Linear Programming Problem graphically: Maximise Z=12 x+18 y subject to the constraints x+y ≤ 1200; x-2 y ≥…2026
• The given graph illustrates:2025
• The given graph illustrates:2025
• Study the given graph. It illustrates:2025
• The graph shown below depicts:2025
• The graph shown below depicts:2025
• Which of the following is not a homogeneous function of x and y?2025
• For a Linear Programming Problem (LPP), the given objective function is Z=x+2 y. The feasible region PQRS determined by the set…2025
• For a Linear Programming Problem (LPP), the given objective function Z=3 x+2 y is subject to constraints: x+2 y ≤ 10; 3 x+y ≤ 15;…2025
• A factory produces two products X and Y. The profit earned by selling X and Y is represented by the objective function Z=5 x+7 y,…2025
• If the feasible region of a linear programming problem with objective function Z=a x+by, is bounded, then which of the following…2025
• The corner points of the feasible region in graphical representation of a L. P. P. are (2,72), (15,20) and (40,15). If Z=18 x+9 y…2025asked 2×
• In a Linear Programming Problem (LPP), the objective function Z=2 x+5 y is to be maximised under the following constraints: x+y ≤…2025
• The corner points of the feasible region of a Linear Programming Problem are (0,2),(3,0),(6,0),(6,8) and (0,5). If Z=ax+by;(a,…2025
• Assertion: The shaded portion of the graph represents the feasible region for the given Linear Programming Problem (LPP). Min…2025
• Assertion: Every point of the feasible region of a Linear Programming Problem is an optimal solution. Reason (R): The optimal…2025
• Assertion: In a Linear Programming Problem, if the feasible region is empty, then the Linear Programming Problem has no solution.…2025
• In a Linear Programming Problem, the objective function Z=5 x+4 y needs to be maximised under constraints 3 x+y ≤ 6, x ≤ 1, x, y…2025
• In a Linear Programming Program (LPP) for objective function Z=14 x-10 y subject to constraints x+y ≤ 8; 3 x-2 y ≥-6; x, y ≥ 0…2025
• For a Linear Programming Problem, find min Z=5 x+3 y (where Z is the objective function) for the feasible region shaded in the…2025
• Solve the following linear programming problem graphically: Maximize Z=8 x+9 y Subject to the constraints: 2 x+3 y ≤ 6; 3 x-2 y ≤…2025
• Solve the following linear programming problem graphically: Maximise Z=x+2 y Subject to the constraints: x-y ≥ 0; x-2 y ≥-2; x ≥…2025
• Solve the following linear programming problem graphically: Maximise Z=20 x+30 y Subject to the constraints: x+y ≤ 80; 2 x+3 y ≥…2025
• Solve the following linear programming problem graphically: Minimise Z=20 subject to the cc; 3 x+y ≥ 9; x+y ≥ 7; x+2 y ≥ 8; x, y…2025
• The feasible region along with corner points for a linear programming problem are shown in the graph. Write all the constraints…2025
• Solve the following linear programming problem graphically: Minimise Z=x-5 y subject to the constraints: x-y ≥ 0; -x+2 y ≥ 2; x ≥…2025
• In the Linear Programming Problem (LPP), find the point/points giving maximum value for Z=5 x+10 y subject to constraints x+2 y ≤…2025
• Consider the Linear Programming Problem, where the objective function Z=(x+4 y) needs to be minimized subject to constraints 2…2025
• In the Linear Programming Problem for objective function Z=18 x+10 y subject to constraints 4 x+y ≥ 20; 2 x+3 y ≥ 30; x, y ≥ 0…2025
• For the given graph of a Linear Programming Problem, write all the constraints satisfying the given feasible region.2025
• Solve the following Linear Programming Problem using graphical method: Maximise Z=100 x+50 y subject to the constraints 3 x+y ≤…2025
• Solve the following Linear Programming Problem graphically: Minimise Z=3 x+5 y subject to the constraints x+2 y ≥ 10; x+y ≥ 6; 3…2025
• A linear programming problem deals with the optimization of a/an:2024
• The common region determined by all the constraints of a linear programming problem is called:2024
• The restrictions imposed on decision variables involved in an objective function of a linear programming problem are called:2024
• The maximum value of Z=4 x+y for a L.P.P. whose feasible region is given below is:2024
• The number of corner points of the feasible region determined by constraints x ≥ 0, y ≥ 0, x+y ≥ 4 is:2024
• Of the following, which group of constraints represents the feasible region given below?2024
• Assertion: The corner points of the bounded feasible region of a L.P.P. are shown below. The maximum value of Z=x+2 y occurs at…2024
• Solve the following linear programming problem graphically: Maximize z=x+y subject to constraints 2 x+5 y ≤ 100; 8 x+5 y ≤ 200; x…2024
• Solve the following linear programming problem graphically: Minimise z=5 x-2 y subject to the constraints x+2 y ≤ 120; x+y ≥ 60;…2024
• Solve the following linear programming problem graphically: Maximise z=5 x+4 y subject to the constraints x+2 y ≥ 4; 3 x+y ≤ 6;…2024
• Solve the following linear programming problem graphically: Minimize z=600 x+400 y, subject to the constraints x+y ≥ 8; x+2 y ≤…2024
• Solve the following linear programming problem graphically: Maximise z=500 x+300 y, subject to constraints x+2 y ≤ 12; 2 x+y ≤…2024
• The corner points of the feasible region determined by the system of linear constraints are as shown in the following figure: (i)…2024
• Solve the following linear programming problem graphically: Maximise z=4 x+3 y, subject to the constraints x+y ≤ 800; 2 x+y ≤…2024
• Solve the following linear programming problem graphically: Maximise Z=2 x+3 y subject to the constraints: x+y ≤ 6; x ≥ 2; y ≤ 3;…2024
• Solve the following L.P.P. graphically: Maximise Z=x+3 y subject to the constraints: x+2 y ≤ 200; x+y ≤ 150; y ≤ 75; x, y ≥ 02024
• Solve the following L.P.P. graphically: Minimise Z=6 x+3 y Subject to constraints 4 x+y ≥ 80; x+5 y ≥ 115; 3 x+2 y ≤ 150; x, y ≥ 02024
• Solve the following Linear Programming problem graphically: Maximise Z=300 x+600 y Subject to x+2 y ≤ 12 2 x+y ≤ 12; x+5/4 y ≥ 5;…2024
• Solve the following L.P.P. graphically: Maximise Z=60 x+40 y Subject to x+2 y ≤ 12 2 x+y ≤ 12; 4 x+5 y ≥ 20; x, y ≥ 02024
• The month of September is celebrated as the Rashtriya Poshan Maah across the country. Following a healthy and well-balanced diet…2024
• The solution set of the inequation 3 x+5 y<7 is:2023
• Which of the following points satisfies both the inequations 2 x+y ≤ 10 and x+2 y ≥ 8?2023
• The number of feasible solutions of the linear programming problem given as Maximize z=15 x+30 y subject to constraints: 3 x+y ≤…2023
• The objective function Z=a x+ by of an LPP has maximum value 42 at (4,6) and minimum value 19 at (3,2). Which of the following is…2023
• The number of corner points of the feasible region determined by the constraints x-y ≥ 0,2 y ≤ x+2, x ≥ 0, y ≥ 0 is:2023
• The feasible region of a linear programming problem is shown in the figure below: Which of the following are the possible…2023
• Solve the following Linear Programming problem graphically: Maximize: Z=3 x+3.5 y subject to constraints: x+2 y ≥ 240, 3 x+1.5 y…2023
• Solve the following linear programming problem graphically: Maximize P=100 x+5 y subject to the constraints x+y ≤ 300; 3 x+y ≤…2023
• Solve the following linear programming problem graphically: Maximise z=5 x+3 y subject to the constraints 3 x+5 y ≤ 15; 5 x+2 y ≤…2023
• Solve the following linear programming problem graphically: Maximize z=3 x+9 y subject to the constraints x+y ≥ 10; x+3 y ≤ 60; x…2023
• Solve graphically the following linear programming problem: Maximise z=6 x+3 y, subject to the constraints 4 x+y ≥ 80; 3 x+2 y ≤…2023
• Solve the following linear programming problem graphically: Maximize: Z=x+2 y subject to constraints: x+2 y ≥ 100, 2 x-y ≤ 0, 2…2023
• Determine graphically the minimum value of the following objective function: z=500 x+400 y subject to constraints; x+y ≤ 200; x ≥…2023
• Solve the following linear programming problem graphically: Minimise: z=-3 x+4 y subject to the constraints x+2 y ≤ 8; 3 x+2 y ≤…2023
• Solve the following linear programming problem graphically: Maximize z=600 x+400 y subject to the constraints: x+2 y ≤ 12; 2 x+y…2023
• Solve the following linear programming problem graphically: Minimize: Z=5 x+10 y subject to constraints: x+2 y ≤ 120, x+y ≥ 60,…2023
• Solve the following linear programming problem graphically: Minimize z=x+2 y subject to the constraints 2 x+y ≥ 3; x+2 y ≥ 6; x ≥…2023
• Solve the following linear programming problem graphically: Maximise z=-3 x-5 y subject to the constraints -2 x+y ≤ 4; x+y ≥ 3;…2023
• Solve the following Linear Programming Problem graphically: Minimise: Z=60 x+80 y subject to constraints: 3 x+4 y ≥ 8; 5 x+2 y ≥…2023
• Solve the following Linear Programming Problem graphically: Maximize: P=70 x+40 y subject to: 3 x+2 y ≤ 9; 3 x+y ≤ 9; x ≥ 0, y ≥ 02023
• Solve the following Linear Programming Problem graphically:2023

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