Checkpoint: Graphing for Linear Programming Solutions

Graph the system of inequalities. Name all of the vertices and evaluate using the objective function for the minimum and maximum values.

$f (x, y) = - 0.5 x + 1.5 y y \leq \frac{1}{4} x + 5 y \leq - x + 10 y \geq - \frac{3}{5} x + 5 y \geq \frac{1}{2} x - \frac{1}{2}$

$f (0, 5) = - 0.5 (0) + 1.5 (5) = 7.5 maximum f (4, 6) = - 0.5 (4) + 1.5 (6) = 7 f (7, 3) = - 0.5 (7) + 1.5 (3) = 1 f (5, 2) = - 0.5 (5) + 1.5 (2) = 0.5 minimum$

Note

Q: Why do you need to graph the system of inequalities to find the minimum and maximum?
A: Because you need the vertices of the graph to substitute into the objective function.

Q: Is this a bounded or unbounded system? How do you know?
A: This is a bounded system because there is an enclosed region.

You may also use technology to graph the system of inequalities and find the intersection points. However, you must be able to transfer this to the coordinate plane in Checkpoint.