C.  Linear Programming

• Used to solve problems involving resource constraints => constrained optimization, minimization or maximization subject to constraints

Ex. - Minimize cost subject to producing a certain quantity, maximize profit subject to limited resources

Ex. - Advertising mix, portfolio mix, transportation problems, scheduling

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1. Formulating the problem

a.  Decision variables

• Variables under decision maker's control

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b. Objective function

• Function that is maximized or minimized

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c. Contraints

• Limits on decision making

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d. Nonnegativity constraints

• Most variables in business and economics cannot take on negative values

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2. Solving the problem

a. Graphical solution

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b. Excel

• Use Data | Solver

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3. Special situations

a. No feasible solution

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b. Multiple solutions

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4. Sensitivity analysis

• Shadow price (dual value) - change in objective function due to a one unit relaxation of a particular constraint

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5.  Applications

a.  Scheduling

• Integer programming - decision variables have to take on integer values

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b.  Transportation

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