Exam 17: the Simplex Solution Method

Given the following linear programming problem: maximize 4+3 subject to 4+3\leq23 5-\leq5 ,\geq0 What is the value of X1 in the final tableau?

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 X1?

Final tableaus cannot be used to conduct sensitivity analysis.

Solve the following problem using the simplex method. Minimize =3+4+8 Subject to: 2+\geq6 emsp; emsp; emsp; emsp;+2\geq4 emsp; emsp; emsp; emsp;,\geq0

A(n) ________ problem can be identified in the simplex procedure when it is not possible to select a pivot row.

The ________ values are computed by multiplying the cj column values by the variable column values and summing.

The ________ values are contribution to profit for each variable.

If a slack variable has a positive value (is basic) in the optimal solution to a linear programming problem, then the shadow price of the associated constraint

The ________ form of a linear program is used to determine how much one should pay for additional resources.

Given the following linear programming problem: maximize =\ 100+80 subject to +2\leq40 3+\leq60 ,\geq0 How many iterations did we have to perform before reaching the final tableau?

In solving a minimization problem, artificial variables are assigned a ________ in the objective function to eliminate them from the final solution.

The first step in solving a linear programming model manually with the simplex method is to convert the model into standard form.

In the simplex procedure, if cj - zj = 0 for a non-basic variable, this indicates that

The objective function coefficient of an artificial variable for a minimization linear programming problem is:

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 -By how much can the amount of space decrease before there is a change in the profit?

In a ________ problem, artificial variables are assigned a very high cost.

The mathematical steps in the simplex method replicate the process in graphical analysis of moving from one extreme point on the solution boundary to another.

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 -How much time will be used?

In the simplex procedure, if it is not possible to select a pivot row, this indicates that

The variable with the largest positive cj - zj is the ________ variable.