Q.Solve the following linear programming problem graphically: Minimize $Z = 3x + 5y$ subject to the constraints $x \ge 1,\ y \ge 1,\ x + y \le 6$.

Constraints: $x\ge1,\ y\ge1,\ x+y\le6$.

Corner points. Intersection of $x=1$ and $y=1$: $(1,1)$. Intersection of $x=1$ and $x+y=6$: $y=5$, giving $(1,5)$. Intersection of $y=1$ and $x+y=6$: $x=5$, giving $(5,1)$. These three lines bound a triangle with vertices $(1,1),\ (1,5),\ (5,1)$.

Evaluating $Z=3x+5y$: …

Recognize that two of the constraints are simple lower bounds (x≥1, y≥1) rather than lines through the origin, find the three corner points by pairing the three boundary lines two at a t …

Treating $x\ge1$ and $y\ge1$ as if they were $x\ge0,\ y\ge0$ and wrongly including the origin as a candidate corner, even t …