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Chapter 2 Linear Programming: Model Formulation And Graphical Solution
Introduction to Management Science, 10e (Taylor)
Chapter 2 Linear Programming: Model Formulation and Graphical Solution
1) Linear programming is a model consisting of linear relationships representing a firm's decisions given an objective and resource constraints.
2) The objective function is a linear relationship reflecting the objective of an operation.
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3) A constraint is a linear relationship representing a restriction on decision making.
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4) A linear programming model consists of only decision variables and constraints.
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5) A feasible solution violates at least one of the constraints.
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6) Proportionality means the slope of a constraint is proportional to the slope of the objective function.
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7) The terms in the objective function or constraints are additive.
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8) The terms in the objective function or constraints are multiplicative.
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9) The values of decision variables are continuous or divisible.
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10) All model parameters are assumed to be known with certainty.
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11) In linear programming models , objective functions can only be maximized.
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12) All linear programming models exhibit a set of constraints.
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13) Linear programming models exhibit linearity among all constraint relationships and the objective function.
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14) The equation 8xy = 32 satisfies the proportionality property of linear programming.
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15) Objective functions in linear programs always minimize costs.
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16) The feasible solution area contains infinite solutions to the linear program.
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17) There is exactly one optimal solution point to a linear program.
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18) The following equation represents a resource constraint for a maximization problem: X + Y ≥ 20
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19) A minimization model of a linear program contains only surplus variables.
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20) In the graphical approach, simultaneous equations may be used to solve for the optimal solution point.
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21) Slack variables are only associated with maximization problems.
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22) Surplus variables are only associated with minimization problems.
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23) If the objective function is parallel to a constraint, the constraint is infeasible.
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24) Multiple optimal solutions occur when constraints are parallel to each other.
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25) Graphical solutions to linear programming problems have an infinite number of possible objective function lines.
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26) The first step in formulating a linear programming model is to define the objective function.
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27) __________ are mathematical symbols representing levels of activity.
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28) The __________ is a linear relationship reflecting the objective of an operation.
Answer
29) A __________ is a linear relationship representing a restriction on decision making.
Answer: constraint
30) If at least one constraint in a linear programming model is violated the solution is said to be __________.
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31) A graphical solution is limited to solving linear programming problems with __________ decision variables
Answer
32) The __________ solution area is an area bounded by the constraint equations.
Answer: feasible
33) Multiple optimal solutions can occur when the objective function line is __________ to a constraint line.
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34) When a maximization problem is __________, the objective function can increase indefinitely without reaching a maximum value.
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35) A linear programming problem that results in a solution that is __________ usually indicates that the linear program has been incorrectly formulated.
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36) In a constraint the __________ variable represents unused resources.
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37) If the objective function is parallel to a constraint, the linear program could have __________.
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38) Corner points on the boundary of the feasible solution area are called __________ points.
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39) The __________ step in formulating a linear programming model is to define the decision variables.
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40) The __________ property of linear programming models indicates that the values of all the model parameters are known and are assumed to be constant.
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41) The __________ property of linear programming models indicates that the rate of change or slope of the objective function or a constraint is constant.
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42) The __________ property of linear programming models indicates that the decision variables cannot be restricted to integer values and can take on any fractional value.
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43) The constraint, 2X +XY violates the __________ property of linear programming.
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44) Consider the following minimization problem:
Min z = x1 + 2x2
s.t. x1 + x2 ≥ 300
2x1 + x2 ≥ 400
2x1 + 5x2 ≤ 750
x1, x2 ≥ 0
What is the optimal solution?
Answer:
45) Consider the following minimization problem:
Min z = x1 + 2x2
s.t. x1 + x2 ≥ 300
2x1 + x2 ≥ 400
2x1 + 5x2 ≤ 750
x1, x2 ≥ 0
Which constraints are binding at the optimal solution? (x1 =250, x2 = 50)
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