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3.4: Linear Programming

Linear Programming. Example: Suppose a Cost function is given by: C = 2x 4y and we have the constraints:x > 0, y > 0 and-x 3y < 15, 2x y < 12(Use x

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3.4: Linear Programming

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    1. 3.4: Linear Programming Intro: Oftentimes we want to optimize a situation - this means to: find a maximum value (such as maximizing profits) find a minimum value (such as minimizing costs). Linear Programming: Process of optimization on a linear function Constraints: Boundaries (borders) on our function Solution Set: called Feasible Region; shaded area of possibilities given our function and our constraints.

    2. Linear Programming Example: Suppose a Cost function is given by: C = 2x + 4y and we have the constraints: x > 0, y > 0 and -x + 3y < 15, 2x + y < 12 (Use x & y intercepts to graph) Find the feasible region. Solution: We already know that x > 0 and y > 0 guarantee us an answer in the first quadrant. So lets look at the other two.

    3. Linear Programming Since our answer has to be in the first quadrant, we know the feasible region is:

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