Exam 13: Introduction to Optimization Modeling

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When formulating a linear programming spreadsheet model,there is one target (objective)cell that contains the value of the objective function.

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When formulating a linear programming spreadsheet model,we specify the constraints in a Solver dialog box,since Excel does not show the constraints directly.

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If a constraint has the equation If a constraint has the equation   ,then the constraint line passes through the points (0,20)and (30,0): ,then the constraint line passes through the points (0,20)and (30,0):

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In some cases,a linear programming problem can be formulated such that the objective can become infinitely large (for a maximization problem)or infinitely small (for a minimization problem).This type of problem is said to be:

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If a manufacturing process takes 3 hours per unit of x and 5 hours per unit of y and a maximum of 100 hours of manufacturing process time are available,then an algebraic formulation of this constraint is:

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All optimization problems have:

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Linear programming models have three important properties.They are:

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There are two primary ways to formulate a linear programming problem,the traditional algebraic way and in spreadsheets.

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Reduced costs indicate how much the objective coefficient of a decision variable that is currently 0 or at its upper bound must change before that the value of that variable changes.

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It helps to ensure that Solver can find a solution to a linear programming problem if the model is well-scaled; that is,all of the numbers are of roughly the same magnitude.

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All linear programming problems should have a unique solution,if they can be solved.

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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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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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What are the decision variables in this problem?

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What are the constraints in this problem?

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There is often more than one objective in linear programming problems

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

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Write out an algebraic expression for the objective function in this problem.

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If a solution to an LP problem satisfies all of the constraints,then is must be feasible.

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Consider the following linear programming problem: Maximize Consider the following linear programming problem: Maximize   Subject to       The above linear programming problem: Subject to Consider the following linear programming problem: Maximize   Subject to       The above linear programming problem: Consider the following linear programming problem: Maximize   Subject to       The above linear programming problem: Consider the following linear programming problem: Maximize   Subject to       The above linear programming problem: The above linear programming problem:

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