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A feasible solution violates at least one of the constraints

07/01/2021 Client: saad24vbs Deadline: 24 Hours

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.


Answer:


3) A constraint is a linear relationship representing a restriction on decision making.


Answer:


4) A linear programming model consists of only decision variables and constraints.


Answer:


5) A feasible solution violates at least one of the constraints.


Answer:


6) Proportionality means the slope of a constraint is proportional to the slope of the objective function.


Answer:


7) The terms in the objective function or constraints are additive.


Answer:


8) The terms in the objective function or constraints are multiplicative.


Answer:


9) The values of decision variables are continuous or divisible.


Answer:


10) All model parameters are assumed to be known with certainty.


Answer:


11) In linear programming models , objective functions can only be maximized.


Answer:


12) All linear programming models exhibit a set of constraints.


Answer:


13) Linear programming models exhibit linearity among all constraint relationships and the objective function.


Answer:


14) The equation 8xy = 32 satisfies the proportionality property of linear programming.


Answer:


15) Objective functions in linear programs always minimize costs.


Answer:


16) The feasible solution area contains infinite solutions to the linear program.


Answer:


17) There is exactly one optimal solution point to a linear program.


Answer:


18) The following equation represents a resource constraint for a maximization problem: X + Y ≥ 20


Answer:


19) A minimization model of a linear program contains only surplus variables.


Answer:


20) In the graphical approach, simultaneous equations may be used to solve for the optimal solution point.


Answer:


21) Slack variables are only associated with maximization problems.


Answer:


22) Surplus variables are only associated with minimization problems.


Answer:


23) If the objective function is parallel to a constraint, the constraint is infeasible.


Answer:


24) Multiple optimal solutions occur when constraints are parallel to each other.


Answer:


25) Graphical solutions to linear programming problems have an infinite number of possible objective function lines.


Answer:


26) The first step in formulating a linear programming model is to define the objective function.


Answer:


27) __________ are mathematical symbols representing levels of activity.


Answer:


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 __________.


Answer:


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.


Answer:


34) When a maximization problem is __________, the objective function can increase indefinitely without reaching a maximum value.


Answer:


35) A linear programming problem that results in a solution that is __________ usually indicates that the linear program has been incorrectly formulated.


Answer:


36) In a constraint the __________ variable represents unused resources.


Answer:


37) If the objective function is parallel to a constraint, the linear program could have __________.


Answer:


38) Corner points on the boundary of the feasible solution area are called __________ points.


Answer:


39) The __________ step in formulating a linear programming model is to define the decision variables.


Answer:


40) The __________ property of linear programming models indicates that the values of all the model parameters are known and are assumed to be constant.


Answer:


41) The __________ property of linear programming models indicates that the rate of change or slope of the objective function or a constraint is constant.


Answer:


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.


Answer:


43) The constraint, 2X +XY violates the __________ property of linear programming.


Answer:


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)


Answer:

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