## Graphical method of solution of Linear programming problems - Basic Level

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
Solution
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
Solution
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)
Solution
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
Solution
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
Solution
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
Solution
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)
Solution
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
Solution
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
Solution
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
Solution
The maximum value of P subject to the constraints is 440

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