Exam 2: An Introduction to Linear Programming

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In which part(s)of a linear programming formulation would the decision variables be stated?

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Find the complete optimal solution to this linear programming problem. Find the complete optimal solution to this linear programming problem.

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Solve the following linear program graphically. Solve the following linear program graphically.

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Does the following linear programming problem exhibit infeasibility,unboundedness,or alternative optimal solutions? Explain. Does the following linear programming problem exhibit infeasibility,unboundedness,or alternative optimal solutions? Explain.

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The optimal solution to any linear programming problem is the same as the optimal solution to the standard form of the problem.

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Find the complete optimal solution to this linear programming problem. Find the complete optimal solution to this linear programming problem.

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Solve the following linear program graphically. Solve the following linear program graphically.

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A constraint that does NOT affect the feasible region of the solution is a

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No matter what value it has,each objective function line is parallel to every other objective function line in a problem.

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Whenever all the constraints in a linear program are expressed as equalities,the linear program is said to be written in

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At a problem's optimal solution,a redundant constraint will have zero slack.

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Solve the following linear program graphically.How many extreme points exist for this problem? ​ Solve the following linear program graphically.How many extreme points exist for this problem? ​   ​

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The Sanders Garden Shop mixes two types of grass seed into a blend.Each type of grass has been rated (per pound)according to its shade tolerance,ability to stand up to traffic,and drought resistance,as shown in the table.Type A seed costs $1 and Type B seed costs $2.​ The Sanders Garden Shop mixes two types of grass seed into a blend.Each type of grass has been rated (per pound)according to its shade tolerance,ability to stand up to traffic,and drought resistance,as shown in the table.Type A seed costs $1 and Type B seed costs $2.​   ​  a.If the blend needs to score at least 300 points for shade tolerance,400 points for traffic resistance,and 750 points for drought resistance,how many pounds of each seed should be in the blend? b.Which targets will be exceeded? c.How much will the blend cost? ​ a.If the blend needs to score at least 300 points for shade tolerance,400 points for traffic resistance,and 750 points for drought resistance,how many pounds of each seed should be in the blend? b.Which targets will be exceeded? c.How much will the blend cost?

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Consider the following linear program: Consider the following linear program:   ​  a.Write the problem in standard form. b.What is the feasible region for the problem? c.Show that regardless of the values of the actual objective function coefficients,the optimal solution will occur at one of two points.Solve for these points and then determine which one maximizes the current objective function. ​ a.Write the problem in standard form. b.What is the feasible region for the problem? c.Show that regardless of the values of the actual objective function coefficients,the optimal solution will occur at one of two points.Solve for these points and then determine which one maximizes the current objective function.

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The constraint 5x1 − 2x2 ≤ 0 passes through the point (20,50).

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Which of the following is a valid objective function for a linear programming problem?

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