SOLUTION: find the minumum value of f(x,y)=2x-y+2 for the polygonal convex set determined by this system of inequalities:x>=1, x<=3, y>=0, 1/2x + y<=5. A)0 B)-3 C)3 D)-0.5

Question 209077: find the minumum value of f(x,y)=2x-y+2 for the polygonal convex set determined by this system of inequalities:x>=1, x<=3, y>=0, 1/2x + y<=5.
A)0
B)-3
C)3
D)-0.5
Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
To best visualize this problem, please draw on a standard x-y coordinate system, the area of concern.
.
(1) x>=1,,,, to the right of a vertical line at x=1
.
(2) x<=3,,,,,to the left of a vertical line at x=3
.
(3) y>=0,,,,,,,above a horizontal line at y=0
.
(4) (x/2) +y <= 5,,,,,below a line from (1,4.5) to (3,3.5)
.
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
.
(1,0),,,,,f(x,y) = 4
.
(1, 4.5),,,f(x,y) = -.5
.
(3,3.5),,,,f(x,y) = .5
.
(3,0),,,,,f(x,y) = 8
.
.
.
It appears to be a min at -.5, which is answer (D)
.

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