Checkpoint: Applications of Linear Programming Solutions

Use the graph from Example 5 to complete the Checkpoint.

Suppose the company updated their objective function to $f (x, y) = 5 x - y .$ Explain the maximum number of miles that each type of vehicle can drive now.

Implement

$f (100, 100) = 400 f (100, 900) = - 400 f (600, 400) = 2600 maximum f (400, 100) = 1900$

Explain

A maximum occurs when the box trucks drive 600 miles and the vans drive 400 miles. This is from the ordered pair (600, 400).

Note

Q: What does the shaded region of the graph represent?
A: All possible solutions to the system of inequalities.

Q: Why is it possible for solutions in the shaded region to include fraction or decimal values?
A: Any ordered pair in the shaded region is a solution. This includes points that are not on the grid lines.