Question: Question1. (40points)Youareprovided withthefollowing linearprogram: min z = 3 x + ys.t. 3 x +2 y 6 x +2 y 42 x + y 10 x

Question1.(40points)Youareprovided withthefollowing linearprogram:

minz= 3x+ys.t.

3x+2y6

x+2y42x+y10x4

x,y0

  1. Onthefollowingpage,usethegraphicalsolution methodtoidentify thefeasibleregion.
  2. Findthefeasibleextremepointsandcalculate theirobjectivevalues.

Extremepoint1:

Extremepoint2:

Extremepoint3:

Extremepoint4:

  1. Drawanisocostlinethatpassesthroughthepoint(x=3,y=0)andfindthedirectionofoptimization.
  2. Providetheoptimalsolutionandoptimalobjectivevalue.

Optimalsolution:x= y=

Optimalobjectivevalue:

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