Exam 13: Introduction to Optimization Modeling

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The additivity property of LP models implies that the sum of the contributions from the various activities to a particular constraint equals the total contribution to that constraint.

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There is often more than one objective in linear programming problems

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Consider the following linear programming problem: Minimize 5x1+6x25 x _ { 1 } + 6 x _ { 2 } Subject to x1+2x212x _ { 1 } + 2 x _ { 2 } \geq 12 3x1+2x2243 x _ { 1 } + 2 x _ { 2 } \geq 24 3x1+x2153 x _ { 1 } + x _ { 2 } \geq 15 x1,x20x _ { 1 } , x _ { 2 } \geq 0 The above linear programming problem:

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The equation of the line representing the constraint 20x+10y100020 x + 10 y \leq 1000 Is:

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It is often useful to perform sensitivity analysis to see how,or if,the optimal solution to a linear programming problem changes as we change one or more model inputs.

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When formulating a linear programming spreadsheet model,there is a set of designated cells that play the role of the decision variables.These are called the objective cells.

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The feasible region in all linear programming problems is bounded by:

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In general,the complete solution of a linear programming problem involves three stages: formulating the model,invoking Solver to find the optimal solution,and performing sensitivity analysis.

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The optimal solution to any linear programming model is:

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Every linear programming problem involves optimizing a:

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The divisibility property of LP models simply means that we allow only integer levels of the activities.

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The divisibility property of linear programming means that a solution can have both:

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Linear programming problems can always be formulated algebraically,but not always on spreadsheet.

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One of the things that you can do with linear programming and a spreadsheet model is to develop a user interface to make it easier for someone who is not an expert in using linear programming.The output can be a report that explains the optimal policy in non-technical terms.The type of system being described is called a (n):

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Suppose a firm must at least meet minimum expected demands of 60 for product x and 80 of product y.An algebraic formulation of these constraints is:

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When there is a problem with Solver being able to find a solution,many times it is an indication of a (n):

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In linear programming,sensitivity analysis involves examining how sensitive the optimal solution is to changes in:

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Shadow prices are associated with nonbinding constraints,and show the change in the optimal objective function value when the right side of the constraint equation changes by one unit.

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The term nonnegativity refers to the condition where:

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In an optimization model,there can only be one:

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