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MHT CET202121 Sep 2021Evening ShiftMathematicsLinear ProgrammingActual

The objective function z =4 z +5 y subjective to 2 x + y 7 ; 2 x+3 y 15 ; y 3, x 0 ; y 0 has minimum value at the point.

Options

  1. Aon the line 2 x+3 y=15
  2. Bon X-axis
  3. Con Y-axis
  4. Dorigin

Correct answer

B. on X-axis

Step-by-step solution

We have lines 2 x+y=7,2 x+3 y=15, y=3 Refer figure The required region is shaded. We have A ( 7 2 , 0 ), B ( 15 2 , 0 ) Point of intersection of 2 x+y=7 and y=3 is D=(2,3) aligned & z _ ( A ) =4 ( 7 2 )+5(0)=14+0=14 & z _ ( B ) =5 ( 15 2 )+5(0)=30+0=30 & z _ ( C ) =4(3)+5(3)=12+15=27 & z _ ( D ) =4(2)+5(3)=8+15=23 aligned Hence minimum value occurs at point a which lies on X axis.

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