Math Questions
Explore questions in the Math category that you can ask Spark.E!
The feasible region of a linear programming problem with two unknowns may be bounded or unbounded.
In the final tableau of a simplex method problem, if the problem has a solution, the last column will contain no negative numbers.
Choosing the pivot row by requiring that the ratio associated with that row be the smallest non-negative number insures that the iteration will not take us from a feasible point to a non-feasible point.
The simplex method can be used to solve all linear programming problems that have solutions.
Every minimization linear programming problem can be converted into a standard maximization linear programming problem.
the following is a standard maximum linear programming problem: max: p=x-y-3zs.t: 4x-3y-z≤-3x+y+z≤102x+y-x≤10x≥0, y≥0, z≥0
In the optimal solution to a linear program, there are 20 units of slack for a constraint. From this, we know that a. the dual price for this constraint is 20. b. the dual price for this constraint is 0. c. this constraint must be redundant. d. the problem must be a maximization problem.
In LP, variables do not have to be integer valued and may take on any fractional value. This assumption is called a. proportionality. b. divisibility. c. additivity. d. certainty.
Choosing the pivot column by requiring that it be the column associated with the most negative entry to the left of the vertical line in the last row of the simplex tableau ensures that the iteration will result in the greatest increase, or, at worst, no decrease in the objective function.
the following linear programming problem has an unbounded feasible region min: c=x-ys.t.: 4x-3y≤03x-4y≥0x≥0, y≥0
If the feasible region gets larger due to a change in one of the constraints, the optimal value of the objective function a. must increase or remain the same for a maximization problem. b. must decrease or remain the same for a maximization problem. c. must increase or remain the same for a minimization problem. d. cannot change
A feasible solution to an LP problem a. must satisfy all of the problem's constraints simultaneously. b. need not satisfy all of the constraints, only some of them. c. must be a corner point of the feasible region. d. must give the maximum possible profit.
When alternate optimal solutions exist in an LP problem, then a. the objective function will be parallel to one of the constraints. b. one of the constraints will be redundant. c. two constraints will be parallel. d. the problem will also be unbounded.
the following is a standard maximum linear programming problem: max: -2x-3y-zs.t: 4x-3y+z≤3-x-y-z≤102x+y-z≤10 x≥0, y≥0
An LP problem has a bounded feasible region. If this problem has an equality 1=2 constraint, then a. this must be a minimization problem. b. the feasible region must consist of a line segment. c. the problem must be degenerate. d. the problem must have more than one optimal solution.
In solving a linear program, no feasible solution exists. To resolve this problem, we might a. add another variable. b. add another constraint. c. remove or relax a constraint. d. try a different computer program.
In an LP problem, at least one corner point must be an optimal solution if an optimal solution exists. a. True b. False
Some linear programming problems have exactly two solutions
The solution set of the inequality 2x + 6y ≤ 12 is below the line 2x + 6y = 12.
Which of the following would cause a change in the feasible region? a. Increasing an objective function coefficient in a maximization problem b. Adding a redundant constraint c. Changing the right-hand side of a nonredundant constraint d. Increasing an objective function coefficient in a minimization problem