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COMEDK2023MathematicsLinear Programming

The maximum value of Z=10 x+16 y , subject to constraints x 0, y 0, x+y 12,2 x+y 20 is

Options

  1. A144
  2. B192
  3. C120
  4. D240

Correct answer

B. 192

Step-by-step solution

Given, constraints are x 0, y 0, x+y 12,2 x+y 20 The feasible region is O A B C O . aligned & Z=10 x+16 y & At, O(0,0), Z=10(0)+16(0)=0 & At, A(10,0), Z=10(10)+16(0)=100 & At, B(8,4) Z=10(8)+16(4)=144 & At, C(0,12), Z=10(0)+16(12)=192 aligned Hence, the maximum value of Z is 192 .

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