It appears to be a linear programming optimization problem, but without the objective function, and only the constraints shown.PeroK said:
After thinking about the problem for a bit, the solution would be the set of points in the first octant that satisfy the given inequalities.scottdave said:
That makes some sense. I guess he is supposed to find a range for those "slack variables" which satisfy the "equation" that was made. For 2 dimensions it would be pretty easy to sketch out. 3 or higher... not so easy.Mark44 said:
I think the OP did a lot of unnecessary work by adding in the slack variables. My advice is to solve the system of inequalities exactly as it's given, by graphing the solution set. The first two inequalities define two half-planes that intersect in a line. The 3rd, 4th, and 5th inequalities constrain the solution set to the first octant.scottdave said:
Isn't the use of slack variables standard in pivot table methods?Mark44 said:
Regarding slack variables, I believe that you are making the same mistake that the OP is making in this thread. In post #1, the instruction is "Solve this inequality."haruspex said:
In post #3, the OP gives what appears to be an example provided by the teacher. There are slack variables and pivots, but no evidence of a target expression to be optimised nor any basis on which the pivots are chosen.Mark44 said:
Not necessarily. I believe it's just another example that the OP found. According to post #1, the instruction is to "solve the inequality," which has nothing to do with slack variables or pivot tables.haruspex said:
Since there is no objective function given, I believe the OP thinks he's supposed to work the problem as if it were a linear programming problem -- one in which an objective function is to be optimized in some way, given a set of constraints. All we have here is a system of inequalities, which makes me believe that what the problem says to do is exactly what should be done -- "solve the inequality (sic)."haruspex said:
If we assume that both examples are linear programming problems, then in neither case has the OP given us the full problem. I was unable to open either the Word attachment or the link in post #1.haruspex said:
A linear inequality is an inequality that involves a linear function, which is a function whose graph is a straight line. It is represented using symbols such as <, >, ≤, or ≥, and it compares two expressions using these symbols.
To solve a linear inequality, you need to isolate the variable on one side of the inequality symbol. This is done by using inverse operations, such as addition, subtraction, multiplication, and division, to both sides of the inequality. The solution is the range of values that make the inequality true.
A linear equation is an equation that represents a straight line on a graph, while a linear inequality represents a region on a graph. In a linear equation, the solution is a single point, while in a linear inequality, the solution is a range of values.
To graph a linear inequality, you first need to solve for the variable and then plot the solution on a number line or a coordinate plane. If the inequality is < or >, use an open circle to represent the boundary line, and if the inequality is ≤ or ≥, use a closed circle. Then, shade the region that satisfies the inequality.
Yes, a linear inequality can have infinitely many solutions. This is because the solution is a range of values, and there are infinite numbers within a range. However, there are also cases where a linear inequality has no solution, such as when the inequality is contradictory or impossible.