3.1.4 Linear Programming - Worksheet
Example 1: Graph each feasible region. 1. ≥ ≥ x
2.
3. x y y
x
≥ ≥− ≤ + 0 1
2
y y x y x 0 0
≥− ≤
y y x y
1 0.5 2 2 3
x y x
1
3 3 7
≥ − ≤− +
≤ + ≤− +
1 4
x
6
≤− +
Example 2: Maximize or minimize each objective function . 4. Maximize P = 10 x + 16 y for the constraints from Exercise 1.
5. Minimize P = 3 x + 5 y for the constraints from Exercise 2.
6. Maximize P = 2.4 x + 1.5 y for the constraints from Exercise 3.
Example 3: 7. Dr. Lee’s dentist practice is open for 7 hours each day. His receptionist schedules appointments, allowing 1 2 hour for a cleaning and 1 hour to fill a cavity. He charges $40 for a cleaning and $95 for a filling. Dr. Lee cannot do more than 4 fillings per day. Find the number of each type of appointment that maximizes Dr. Lee’s income for the day.
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