3.1 Review Worksheet (continued)
Graph the system of inequalities and classify the figure created by the solution region. 32. ≥ x 0 33. 2.5 34. 6 35.
y x y x y
y x y x
y y
≤ ≤− + ≥ 0
≤ + ≥ +
≤ ≥−
2
1 3
1
0.5
− + ≥− x y
4
y x y x
y x y x
6 1
8 2 4
≤− + ≥− −
≤− + ≤ +
1 3
x y
1
+ ≤−
3.1.4 Linear Programming Graph each feasible region. 36. ≥ ≥ ≥ − ≤ + x y y x y x 0 0 4 4 5
37.
38.
x x
x
0 5
0
≥ ≤
≤
y y y
≥ ≤ ≥− − x 0 9
y x y x 1 5
3
≥ −
2 7
4
≤− +
Maximize or minimize each objective function. 39. Maximize P = − 21 x + 11 y for the constraints from Exercise 36.
40. Minimize P = − 2 x − 4 y for the constraints from Exercise 37.
41. Maximize P = x + 3 y for the constraints from Exercise 38.
178
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