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COMEDK2023MathematicsLinear Programming

The maximum value of Z=12 x+13 y , subject to constraints x 0, y 0, x+y 5 and 3 x+y 9 is

Options

  1. A63
  2. B65
  3. C60
  4. D117

Correct answer

B. 65

Step-by-step solution

Given constraints are x 0, y 0, x+y 5 and 3 x+y 9 and z=12 x+13 y The feasible region is O A B C O . aligned & Z=12 x+13 y & At, O(0,0), Z=12(0)+13(0)=0 & At, A(3,0), Z=12(3)+13(0)=36 & At, B(2,3), Z=12(2)+13(3)=63 & At, C(0,5), Z=12(0)+13(5)=65 aligned Here, maximum value of Z is 65 .

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