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MHT CET20243 May 2024Evening ShiftMathematicsArea Under CurvesActual

The maximum value of Z =x+y , subjected to x+y 10,5 x+3 y 15, x 6, x, y 0

Options

  1. Aoccurs only at unique point
  2. Boccurs only at two distinct points
  3. Coccurs at infinitely many points
  4. Ddoes not exist

Correct answer

C. occurs at infinitely many points

Step-by-step solution

Feasible region lies on the origin side of x+y=10, x=6 and non-origin side of 5 x+3 y=15 The corner points of feasible region are A (0,5) and B (0,10), C (6,4), D (6,0), E (3,0) At A (0,5), z =0+5=5 At B( 0,10 ), z =0+10=10 At C(6,4), z=6+4=10 At D (6,0), z =6+0=6 At E(3,0), z=3+0=3 z has maximum value at B (0,10) and C (6,4) . z has infinite solution on seg BC .

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