Explanation:
the best way is simply to draw the lines by using "=" instead of the inequality signs.
and then use the original inequality signs to determine which sides of the lines are valid. for ">=" it usually means the right-upper side.
x>=0, y>=0 means we are only looking at the first quadrant (the upper right one, where x and y values are both positive).
the minimum of the main line (c = 2x + 3y) is where 0 = 2x + 3y touches the crossing point of 4x +3y = 29 and x + 2y = 11, when we move 0 = 2x + 3y in parallel up or down.
without the ability to draw we can calculate that crossing point :
4x + 3y = 29
x + 2y = 11
we e.g. multiply the 2nd equation by -4 and then add both :
4x + 3y = 29
- 4x - 8y = -44
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0 -5y = -15
y = -15/-5 = 3
x + 2×3 = 11
x + 6 = 11
x = 5
this crossing point must be the minimum, as the value points of both inequalities are above their limit lines.
so, the minimum of
C = 2x + 3y = 2×5 + 3×3 = 19