Answer
Maximum: 198
Minimum: 195
Work Step by Step
For linear optimization problems, the maximum and minimum will always occur at a corner of the feasibility area. Therefore, we only need to focus on the points (0,2), (0,5), and (4,0). Now, we just plug in x and y into $M = 200 - x - y$ and find the largest and smallest values:
At (0,2): M = 200 - 0 - 2 = 198
At (0,5): M = 200 - 0 - 5 = 195
At (4,0): M = 200 - 4 - 0 = 196
Comparing our results, we know that in the given region, the maximum of $M = 200 - x - y$ is 198, and the minimum is 195.
