Graphical method of solution of Linear programming problems - Basic Level

Dear Readers,

Linear programming is a method to achieve the best outcome in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming. .

Q1. The L.P. problem Max z=x1 + x2, such that -2x1 + x2 <= 1, x1 <= 2, x1 + x2 <= 3 and x1,x2 >= 0 has
  •  One solution
  •  Three solution
  •  An infinite number of solutions
  •  None of these
The L.P. problem Max z=x1 + x2, such that -2x1 + x2 <= 1, x1 <= 2, x1 + x2 <= 3 and x1,x2 >= 0 has an infinite number of solutions

Q2.On maximizing z = 4x + 9y subject to x + 5y <= 200,2x + 3y <= 134 and x,y >= 0, z =
  •  380
  •  382
  •  384
  •  None of these
z is equal to 382

Q3.  The point at which the maximum value of (3x + 2y) subject to the constraints x + y <= 2, x >= 0,y >= 0 is obtained, is
  •  (0,0)
  •  (1.5,1.5)
  •  (2,0)
  •  (0,2)
The point is (2,0)

Q4. The solution of a problem to maximize the objective function z=x+2y under the constraints x-y <= 2, x+y <=4 and x,y >= 0 , is
  •  x=0,y=4,z=8
  •  x=1,y=2,z=5
  •  x=1,y=4,z=9
  •  x=0,y=3,z=6
The solution is x=0,y=4,z=8

Q5.The maximum value of p=6x + 8y subject to constraints 2x + y <= 30, x + 2y <= 24 and x >= 0, y >= 0 is
  •  90
  •  120
  •  96
  •  240
 The maximum value of P is 120

Q6. The maximum value of P = x+3y such that 2x + y <= 20, x + 2y <= 20, x >= 0 , y >= 0, is
  •  10
  •  60
  • 30
  •  None of these
The maximum value of P is 30

Q7.The point at which the maximum value x + y, of subject to the constraints x + 2y <= 70, 2x + y <= 95, x,y >= 0 is obtained, is
  •  (30,25)
  •  (20,35)
  •  (35,20)
  •  (40,15)
The point is (40,15)

Q8.The maximum value of the objective function P = 5x + 3y, subject to the constraints x >= 0, y >= 0 and 5x + 2y <= 10 is
  •  6
  •  10
  •  15
  •  25
The maximum value of the objective function subject to the constraints is 15

Q9. The maximum value of P = 8x + 3y, subject to the constraints x+y <= 3, 4x + y <= 6, x >= 0, y >= 0 is
  •  9
  •  12
  •  14
  •  16
The maximum value of p = 8x+3y, subject to the constraints is 14

Q10. The maximum value of P=6x+11y subject to the constraints 2x+y <= 104 , x+2y <= 76 and x>=0 , y>=0 is
  •  240
  •  540
  •  440
  •  None of these
The maximum value of P subject to the constraints is 440

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Graphical method of solution of Linear programming problems - Basic Level
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