The maximum value of P is 13, which occurs at the point (5, 1.5) within the bounded region defined by the constraints.
Graphing constraints:
Plot x≤5, y≥0, x+y≥1, and 4y-x≤1, creating a bounded region.
Vertices:
Find the vertices as (0.6, 0.4), (5, 1.5), (1, 0), and (5, 0).
Evaluating P:
Calculate P for each vertex:
P(0.6, 0.4) = 4.2
P(5, 1.5) = 13
P(1, 0) = -1
P(5, 0) = -5
Comparison: P(5, 1.5) yields the highest value, 13.
The maximum value of P is 13, which occurs at the point (5, 1.5) within the bounded region defined by the constraints.