Exam 17: the Simplex Solution Method

The theoretical limit on the number of decision variables that can be handled by the simplex method is 50.

At the initial basic feasible solution at the origin, only slack variables have a value greater than zero.

For a maximization linear programming problem, a(n) ________ is ________ for a less-than-or-equal-to constraint.

Given the following linear programming problem: maximize =\ 100+80 subject to +2\leq40 3+\leq60 ,\geq0 Using the simplex method, what is the optimal value for X2?

The simplex method moves from one better solution to another until the best one is found, and then it stops.

________ variables are added to constraints and represent unused resources.

In using the simplex method, the number of basic variables is equal to the number of constraints.

In the simplex method, the model is put into the form of a table, and then a number of mathematical steps are performed on the table.

The linear programming problem whose output follows determines how many red nail polishes, blue nail polishes, green nail polishes, and pink nail polishes a beauty salon should stock. The objective function measures profit; it is assumed that every piece stocked will be sold. Constraint 1 measures display space in units, constraint 2 measures time to set up the display in minutes. Constraints 3 and 4 are marketing restrictions. MAX    100x1 + 120x2 + 150x3 + 125x4 Subject to    1. x1 + 2x2 + 2x3 + 2x4 ? 108       2. 3x1 + 5x2 + x4 ? 120       3. x1 + x3 ? 25       4. x2 + x3 + x4 > 50       x1, x2, x3, x4 ? 0 Optimal Solution: Objective Function Value = 7475.000 Variable Value Reduced Costs X1 8 0 X2 0 5 X3 17 0 X4 33 0 Constraint Slack/Surplus Dual Prices 1 0 75 2 63 0 3 0 25 4 0 -25 Objective Coefficient Ranges Variable Lower Limit Current Value Upper Limit X1 87.5 100 none X2 none 120 125 X3 125 150 162 X4 120 125 150 Right Hand Side Ranges Constraint Lower Limit Current Value Upper Limit 1 100 108 123.75 2 57 120 none 3 8 25 58 4 41.5 50 54 -To what value can the profit on red nail polish drop before the solution would change?

Slack variables are added to ________ constraints and represent unused resources.