Answer
Maximum: 161
Minimum: 135
Work Step by Step
The graph below shows the feasible area formed by the intersection of all the inequalities. The corners of the feasible area are also shown.
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 (0,0), (0,7), (2,6), and (5,0). Now, we just plug in x and y into P = 140-x+3y and find the largest and smallest values:
At (0,0): P = 140 - 0 + 3(0) = 140
At (0,7): P = 140 - 0 + 3(7) = 161
At (2,6): P = 140 - 2 + 3(6) = 156
At (5,0): P = 140 - 5 + 3(0) = 135
Comparing our results, we know that in the given region, the maximum of P = 140-x+3y is 161, and the minimum is 135.
