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BITSAT2018MathematicsLinear ProgrammingActual

The coordinates of the point at which minimum value of Z = 7 x - 8 y subject to constraints x + y - 20 ≤ 0 , y ≥ 5 , x ≥ 0 , y ≥ 0 is attained, is

Options

  1. A20 , 0
  2. B15 , 5
  3. C0 , 5
  4. D0 , 20

Correct answer

D. 0 , 20

Step-by-step solution

Feasible region is A B C A and Z = 7 x - 8 y At A 0 , 5 ,   Z = 7 × 0 - 8 × 5 = - 40 At B 15 , 5 ,   Z = 7 15 - 8 5 = 65 At C 0 , 20 ,   Z = 7 0 - 8 20 = - 160 Hence, the minimum value of Z is attained at point 0 , 20 So, option d is correct.

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