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8.6 Linear Programming
Vocabulary for this section:
To solve a linear program:
1. Solve the system of linear inequalies.
2. Determine the coordinates of the verces of the feasible region.
3. Evaluate the objecve funcon at each vertex.
4. Idenfy the maximum or minimum value of the objecve funcon.
Example 1: Determine the value of x and y that will maximize the objecve funcon under the constraints:
Example 2: Determine the value of x and y that will minimize the objecve funcon under the constraints:
If a feasible region is a polygon, then the objecve funcon…
If a feasible region is unbounded, then the objecve funcon…
The type of problems that are solved using linear programming are called
________________________.
Example 3: A total of 44 planes were available on a given day during the Berlin Airli following WWII. Some planes were large and some were small. The large planes required four‐person crews and the small planes required two‐person crews, selected from a total of 128 crew members. A large plane could carry 30,000 3 of cargo and a small plane could carry 20,000 3. How many planes of each type are needed to maximize the cargo space?
Let x represent the number of large planes and y the number of small planes. Organized the informaon from the problem in the table below: