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MHT CET202310 May 2023Evening ShiftMathematicsMathematical InductionActual

The shaded area in the figure given below is a solution set of a system of inequations. The minimum value of objective function 3 x+5 y , subject to the linear constraints given by this system of inequations is

Options

  1. A19.5
  2. B2
  3. C195
  4. D19.8

Correct answer

A. 19.5

Step-by-step solution

Let the corner points of the feasible region be A, B , C , D . Solving equations y=, 3 and 2 x+3 y=12 , we get A =(1.5,3) Similarly, aligned & B =(4,3) & C =(4,7) & D = ( 3 5 , 18 5 ) aligned Let Z=3 x+5 y Value of Z at point A=19.5 Value of Z at point B=27 Value of Z at point C=47 Value of Z at point D= 99 5 The minimum value of Z is 19.5 .

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