Checkpoint: Optimization Solutions

Label all of the vertices on the graph. Then find the minimum and maximum values using the objective function: $f (x, y) = 2 x + y .$

$f (0, 7) = 2 (0) + (7) = 7 f (8, 2) = 2 (8) + (2) = 18 maximum f (5, 0) = 2 (5) + (0) = 10 f (0, 4) = 2 (0) + (4) = 4 minimum$

Note

To continue past this Checkpoint, students should confidently and correctly answer this problem.

Q: Can you determine the minimum and maximum by only looking at the graph? Explain.
A: No, you have to use the objective function and the vertices of the graph together.

To extend this problem, you can determine the 4 inequalities that form the shaded region, then check using technology.

$x \geq 0, y \leq - \frac{5}{8} x + 7, y \geq \frac{2}{3} x - \frac{10}{3}, y \geq - \frac{4}{5} x + 4$