Homework 3 + 4 Study Set

25 July 2022
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question
To solve a linear programming problem with thousands of variables and constraints: a) a personal computer can be used b) a mainframe computer is required c) the problem must be partitioned into subparts d) graphical method can be used
answer
A (a personal computer can be used)
question
A dual value (shadow price) for a constraint in a maximization problem means: a) as the right hand side value decreases, the objective value function will increase b) as the right hand side value increases, the objective value function will increase c) as the right hand side value increases, the objective value function will decrease d) as the right hand side value increases, the objective value function value will stay the same
answer
B (as the right hand side value increases, the objective value function will increase)
question
If a decision variable is not positive in the optimal solution, its reduced cost is: a) what its objective function value would need to be before it could become positive b) the amount the decision variable coefficient would need to improve before it could become positive c) the amount the decision variable coefficient would need to improve before it could become negative d) zero
answer
B (the amount the decision variable coefficient would need to improve before it could become positive)
question
A constraint with a positive slack value: a) will have a positive dual value (shadow price) b) will have a negative dual value (shadow price) c) will have a dual value (shadow price) of zero d) has no restrictions for its dual price
answer
C (will have a dual value (shadow price) of zero)
question
The range of feasibility measures which of the following: a) the right hand side values for which the objective function value will not change b) the right hand side values for which the values of the decision variables will not change c) the right hand side values for which the dual values (shadow prices) will not change d) the right hand side values for which the dual prices will change
answer
C (the right hand side values for which the dual values (shadow prices) will not change)
question
Variable = 1 Allowable Increase = 40 Current Value (coefficient) = 100 Allowable Decrease = 20 What will happen to the solution if the objective function coefficient for variable 1 is changed to 50? a) nothing. The values of the decision variables and the objective function will all remain the same. b) the objective function value and the decision variables values will change c) the objective function value will change, but the decision variable values will remain the same d) the dual value (shadow price) will change
answer
B (the objective function value and the decision variables values will change)
question
Constraint = 2 Allowable Decrease = 60 Current Value = 300 Allowable Increase = 120 What will happen if the right hand side for constraint 2 is changed to 400? a) nothing. The values of the decision variables, the dual prices, and the objective function will all remain the same b) the corresponding dual value (shadow price) will remain the same and the objective function value will change c) the same decision variable will be positive, but their values, the objective function value, and the dual prices will change d) the problem will need to be resolved to find the new optimal solutions
answer
B (the corresponding dual value (shadow price) will remain the same and the objective function value will change)
question
Sensitivity analysis information in computer output is based on the assumption of: a) no coefficient change b) one coefficient change c) two coefficient change d) all coefficient change
answer
B (one coefficient change)
question
If a decision variable's optimal solution value is zero, its reduced cost is not zero. T/F
answer
True
question
If a decision variable's optimal solution value is positive, its reduced cost is zero. T/F
answer
True
question
If a decision variable's optimal solution value is negative, its reduced cost is zero. T/F
answer
False
question
If a decision variable's optimal solution value is zero, its reduced cost is zero. T/F
answer
False
question
If a decision variable's optimal solution value is negative, its reduced cost is positive. T/F
answer
False
question
If a decision variable's optimal solution value is zero, its dual value is positive. T/F
answer
False
question
If a constraint has a positive slack variable value, that means the right hand side value are not fully used. T/F
answer
True
question
A positive slack variable value represents the amount of used right hand side value. T/F
answer
False
question
A negative slack variable value represents the amount of used right hand side value. T/F
answer
False
question
If a slack variable value is positive, its dual value (shadow price) is zero T/F
answer
True
question
If a slack variable value is zero, its dual value (shadow price) is positive. T/F
answer
True
question
If a dual value is 10, that means the objective function value will improve by 20 if the right hand side value of the corresponding constraint increases by 2 units. T/F
answer
True
question
If a dual value is 20, that means the objective function value will improve by 20 if the right hand side value of the corresponding constraint increases by 2 units. T/F
answer
False
question
If a dual value is zero, that means the objective function value will not change if the right hand side value of the constraint increases by an amount. T/F
answer
True
question
A slack variable is used for constraint with less than or equal to sign. T/F
answer
True
question
Media selection problems usually determine: a) the coverage provided by each media source b) how many times to use each media source c) the cost of each advertising exposure d) the relative value of each medium
answer
B (how many times to use each media source)
question
The objective function for portfolio selection problems usually is maximization of expected return or: a) maximization of investment types b) minimization of risk c) minimization of cost d) maximization of number of stock shares
answer
B (minimization of risk)