Exam 22: Linear Programming: The Simplex Method

Consider the following general form of a linear programming problem: Maximize Profit Subject to: Amount of resource A used ≤ 100 units Amount of resource B used ≤ 240 units Amount of resource C used ≤ 50 units The shadow price for S1 is 25, for S2 is 0, and for S3 is 40.If the right-hand side of constraint 3 were changed from 150 to 151, what would happen to maximum possible profit?

Slack and surplus variables are used in simplex only for the solution of maximization problems.

Sensitivity analysis may be used to

Consider the following linear program: Maximize Z = 3 X1 + 2 X2 - X3 Subject to: X1+ X2 + 2 X3 ≤ 10 2 X1 - X2 + X3 ≤ 20 3 X1 + X2 ≤ 15 X1, X2, X3 ≥ 0 (a)Convert the above constraints to equalities by adding the appropriate slack variables. (b)Set up the initial simplex tableau and solve.

Sensitivity analysis cannot be used to examine the effects of

The constraint 5 X₁ + 6 X₂ ≤ 30, when converted to an = constraint for use in the simplex algorithm, will be 5 X₁ + 6 X₂ - S = 30.

In linear programs with more than two decision variables, the area of feasible solutions is represented by an n-dimensional polyhedron.

Sensitivity testing of basic variables involves reworking the initial simplex tableau.

Which of these statements is best?

The solution to the dual LP problem

Which of these statements is best?

Table M7-2 -According to Table M7-2, which is a summarized solution output from simplex analysis, the optimal solution to this problem is

Shadow prices

Table M7-1 -According to Table M7-1, all of the resources are being used.If the amount of resource A were changed from 64 to 65, then the maximum possible total profit would be

Variables in the solution mix are called

Solve the following linear programming problem using the simplex method. Maximize 3 X1 + 5X2 Subject to: 4 X1 + 3 X2 ≤ 48 X1 + 2 X2 ≤ 20 X1, X2 ≥ 0

If one changes the contribution rates in the objective function of an LP problem

An artificial variable has no physical interpretation but

Table M7-3 -According to Table M7-3, which is the final simplex tableau for a problem with two variables and two constraints, what are the values for all the variables in this solution?

A basic feasible solution to a system of n equations is found by setting n variables equal to 0 and solving for the other variables.