NCERT Class 12 Maths
Chapter 12: Linear Programming
10 Questions Solved
NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming — Exercise 12.1
Click any question below for its step-by-step NCERT textbook solution, concept hints, and worked explanation.
Question 1
Maximize Z=3x+4y subject to x+y≤4, x≥0,y≥0. Solve graphically.
Question 2
Minimize Z=−3x+4y subject to x+2y≤8,3x+2y≤12,x,y≥0. Solve graphically.
Question 3
Maximize Z=5x+3y subject to 3x+5y≤15,5x+2y≤10,x,y≥0. Solve graphically.
Question 4
Minimize Z=3x+5y subject to x+3y≥3,x+y≥2,x,y≥0. Solve graphically.
Question 5
Maximize Z=3x+2y subject to x+2y≤10,3x+y≤15,x,y≥0. Solve graphically.
Question 6
Minimize Z=x+2y subject to 2x+y≥3,x+2y≥6,x,y≥0. Show that the minimum occurs at more than two points. Solve graphically.
Question 7
Minimize and maximize Z=5x+10y subject to x+2y≤120,x+y≥60,x−2y≥0,x,y≥0. Solve graphically.
Question 8
Minimize and maximize Z=x+2y subject to x+2y≥100,2x−y≤0,2x+y≤200,x,y≥0. Solve graphically.
Question 9
Maximize Z=−x+2y subject to x≥3,x+y≥5,x+2y≥6,y≥0. Solve graphically.
Question 10
Maximize Z=x+y subject to x−y≤−1,−x+y≤0,x,y≥0. Solve graphically.