HW #1B
How much per month would an extra 1000 units of wiring time be worth to MS electronics?
$6,000
Which of the following is the wiring time constraint?
0.5MX1 + 1.5MX2 + 3.0MX3 + 1.0MX4 ≤ 16,000
How many of each type of component should MS electronics produce each month and what will the objective function value be?
15884MX1; 500MX2; 2136MX3; & 900MX4. Objective Function: 429940.
An upgrading of machinery planned to start in three months' time will cause a certain amount of disruption and it is thought that the monthly limit on drilling hours will fall by 2400 hours while this work is being done. Having examined the Solver output, MS management are not worried about this. Why?
Because this constraint is non-binding and there is already a slack.
Which of the following is not a question answered by sensitivity analysis?
By how much will the objective function value change if the right-hand side value of a constraint changes beyond the range of feasibility?
From the output, which constraint(s) have surplus?
DEM (MX3) & DEM (MX1)
From the output, which constraint(s) have slack?
Drilling & Assembly
A multiple choice constraint involves selecting k out of n alternatives, where k ≥ 2.
False
The 100 percent rule can be applied to changes in both objective function coefficients and right-hand sides at the same time.
False
The amount of a sunk cost will vary depending on the values of the decision variables.
False
The dual price for a percentage constraint provides a direct answer to questions about the effect of increases or decreases in that percentage.
False
The solution to the LP Relaxation of a minimization problem will always be less than or equal to the value of the integer program minimization problem.
False
There is a dual price for every decision variable in a model.
False
What is the objective function for this problem?
Max Profit = 20MX1 + 30MX2 + 35MX3 + 25MX4
Constraint: 2 Lower Limit: 240 Current Value: 300 Upper Limit: 420 What will happen if the right-hand-side for constraint 2 increases by 200?
The problem will need to be resolved to find the new optimal solution and dual price.
Variable: 1 Lower Limit: 60 Current Value: 100 Upper Limit: 120 What will happen to the solution if the objective function coefficient for variable 1 decreases by 20?
The value of the objective function will change, but the values of the decision variables and the dual prices will remain the same.
MS electronics think that a change in manufacturing location could increase profits by reducing costs. The following scenario is thought to be possible: unit profit for the MX2 increases by 30% and simultaneously the MX3 increases by 20%. How would these changes impact the optimal solution?
These changes are not allowed. The problem will need to be resolved to find the new optimal solution.
Unexpectedly, monthly demand for the MX2 falls to 400 units. How will this change impact the optimal solution?
This change is allowed. The new objective function will increase by 960.
A large number of staff will be leaving next month and, if no replacements can be found, 360 hours of finishing time will be lost. How would this affect the optimal solution?
This change is allowed. The value of the objective function will decrease by $12,240 ($34*360).
MS electronics think that a change in manufacturing location could increase profits by reducing costs. The following scenario is thought to be possible: the only change is that the unit profit for the MX2 increases by 20%. How would this change impact the optimal solution?
This change is allowed. The value of the objective function will increase by $3,000.
MS electronics think that a change in manufacturing location could increase profits by reducing costs. The following scenario is thought to be possible: the only change is that the unit profit for the MX4 increases by 10%. How would this change impact the optimal solution?
This change is not allowed. The problem will need to be resolved to find the new optimal solution.
One MS manager pointed out that there is a slight risk that the reduction in drilling hours available may be 2700 hours. How should MS management react to this?
This is more than the allowable decrease. The problem need to be resolved to find the impact on the optimal solution.
In general, rounding large values of decision variables to the nearest integer value causes fewer problems than rounding small values.
True
In order to tell the impact of a change in a constraint coefficient, the change must be made and then the model resolved.
True
Some linear programming problems have a special structure that guarantees the variables will have integer values.
True
The classic assignment problem can be modeled as a 0-1 integer program.
True
The objective of the product design and market share optimization problem presented in the textbook is to choose the levels of each product attribute that will maximize the number of sampled customers preferring the brand in question.
True
The reduced cost for a positive decision variable is 0.
True
MS are offered an extra 2100 hours of wiring time per month at a total monthly cost of $11,000. Should MS accept the offer?
Yes. An extra of 2100 is allowed and worth $6*2100 = $12,600 ≥ $11,000, thus, MS should accept the offer.
The 0-1 variables in the fixed cost models correspond to
a process for which a fixed cost occurs.
Rounding the solution of an LP Relaxation to the nearest integer values provides
an integer solution that might be neither feasible nor optimal.
A negative dual price for a constraint in a minimization problem means
as the right-hand side increases, the objective function value will increase.
If the acceptance of project A is conditional on the acceptance of project B, and vice versa, the appropriate constraint to use is a
co-requisite constraint.
Sensitivity analysis for integer linear programming
does not have the same interpretation and should be disregarded.
Rounded solutions to linear programs must be evaluated for
feasibility and optimality.
To perform sensitivity analysis involving an integer linear program, it is recommended to
make multiple computer runs.
When the cost of a resource is sunk, then the dual price can be interpreted as the
maximum amount the firm should be willing to pay for one additional unit of the resource.
The graph of a problem that requires x1 and x2 to be integer has a feasible region
of dots.
Sensitivity analysis information in computer output is based on the assumption of
one coefficient changes.
Most practical applications of integer linear programming involve
only 0-1 integer variables and not ordinary integer variables.
The 100% Rule compares
proposed changes to allowed changes.
The amount by which an objective function coefficient can change before a different set of values for the decision variables becomes optimal is the
range of optimality.
The dual value on the non-negativity constraint for a variable is that variable's
reduced cost.
If a decision variable is not positive in the optimal solution, its reduced cost is
the amount its objective function value would need to improve before it could become positive.
The dual price measures, per unit increase in the right hand side of the constraint,
the change in the value of the optimal solution.
An objective function reflects the relevant cost of labor hours used in production rather than treating them as a sunk cost. The correct interpretation of the dual price associated with the labor hours constraint is
the maximum premium (say for overtime) over the normal price that the company would be willing to pay.
The range of feasibility measures
the right-hand-side values for which the dual prices will not change.
Which of the following is the most useful contribution of integer programming?
using 0-1 variables for modeling flexibility
A constraint with a positive slack value
will have a dual price of zero.
Let x1 , x2 , and x3 be 0 - 1 variables whose values indicate whether the projects are not done (0) or are done (1). Which answer below indicates that at least two of the projects must be done?
x1 + x2 + x3 ≥ 2
In a model, x1 ≥ 0 and integer, x2 ≥ 0, and x3 = 0, 1. Which solution would not be feasible?
x1 = 2, x2 = 3, x3 = .578
Let x1 and x2 be 0 - 1 variables whose values indicate whether projects 1 and 2 are not done or are done. Which answer below indicates that project 2 can be done only if project 1 is done?
x1 − x2 ≥ 0
