How many points with integer coordinates lie in the feasible region defined by , 3x+4y\leq 12,\: \: x\geq 0\: \: and\: \: y\geq 1?    

  • Option 1)

    4

  • Option 2)

    5

  • Option 3)

    6

  • Option 4)

    7

 

Answers (1)

3x+4y\leq 12

put x=0,1,2,3,4

and y=0,1,2,3

Now: points are which satisfies 

(0,0), (0,1) (0,2) (0,3)

(1,0), (1,1), (1,2), (2,0), (2,1), (3,0)

but x\geq 0,y\geq 1\\ \therefore (0,1),(0,2), (0,3)(1,1),(1,2)(2,1)


Option 1)

4

This solution is incorrect 

Option 2)

5

This solution is incorrect 

Option 3)

6

This solution is correct 

Option 4)

7

This solution is incorrect 

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