Practice Problem #1
Maximize the given objective function within the given constraints:
Objective Function: R(x, y) = 300x + 250y
Constraints:
x ≥ 0
y ≥ 0
2x + 3y ≤ 60
4x + 3y ≤ 90
Vertices:
(0, 0), (0, 20), (15, 10) and (22.5, 0)
Feasible Region:
Maximum Value:
R(0, 0) = 300(0) + 250(0) = 0
R(0, 20) = 300(0) + 250(20) = 5000
R(15, 10) = 300(15) + 250(10) = 7000
R(22.5, 0) = 300(22.5) + 250(0) = 6750
The maximum value is __ and it occurs when x = __ and y = __
Answer: The maximum value is 7000 and it occurs when x = 15 and y = 10
Practice Problem #2
Minimize the given objective function within the given constraints:
Objective Function: R(x, y) = 5x + y
Constraints:
y ≥ 10
x + y ≤ 100
2x + 5y ≤ 290
4x + y ≥ 130
Vertices:
(20, 50), (30, 10), (90, 10) and (70, 30)
Feasible Region:
Minimum Value:
C(20, 50) = 5(20) - (50) = 50
C(30, 10) = 5(30) - (10) = 140
C(90, 10) = 5(90) - (10) = 440
C(70, 30) = 5(70) - (30) = 320
The minimum value is __ and it occurs when x =__ and y = __
Answer:
The minimum value is 50 and it occurs when x = 20 and y = 50
