Minimize C = x +y with the following constraint O<=X<=4 0<=Y<=4 2X-3Y<=-1 -X+Y>=0

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The thick red lines enclose the given constrained region. The blue line is of the form x+y=c where c is a constant. c has a minimum value when the line is as far over to the left as possible to remain in the enclosed region.

The line 2x-3y=-1 is also 3y-2x=1, and has a y-intercept at y=⅓. The blue line must pass through this intercept to be in its leftmost position. So x+y=⅓ is the equation and c=⅓ is the minimum value.

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