Question 209077
To  best  visualize  this  problem,  please  draw  on  a  standard  x-y  coordinate  system,  the  area  of  concern.
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(1) x>=1,,,,   to  the  right  of  a  vertical  line  at  x=1
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(2) x<=3,,,,,to  the  left  of  a  vertical  line  at  x=3
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(3) y>=0,,,,,,,above  a  horizontal  line  at  y=0
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(4) (x/2) +y <= 5,,,,,below  a  line  from (1,4.5)  to (3,3.5)
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Now,  to  find  the  min of  f(x,y) = 2x -y +2,,,let's  look  at  the  corners  of  the  area  of  concern,,,by  just  substituting coordinate  values  in function
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(1,0),,,,,f(x,y) = 4
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(1, 4.5),,,f(x,y) = -.5
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(3,3.5),,,,f(x,y) = .5
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(3,0),,,,,f(x,y) = 8
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It  appears  to  be  a  min  at  -.5, which  is  answer (D)
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