If the optimal value of the objective function in a linear programming problem exists, then that valu [Select] of the corner points of the feasible region.

The situation in which the value of the solution may be made infinitely large in a maximization linear programming problem or infinitely small in a minimization problem without violating any of the constraints is known as.   The __________ assumption necessary for a linear programming model to be appropriate means that the contribution to the objective function and the amount of resources used in each constraint are in accordance to the value of each decision variable.   In problem formulation, the   a. nonnegativity constraints are always ignored.     b. optimal solution is decided upon.     c. objective is expressed in terms of the decision variables.     d. constraints are expressed in terms of the obtained objective function coefficients.   Which of the following error messages is displayed in Excel Solver when attempting to solve an unbounded problem?

Use the simplex method to solve the linear programming problem. Maximize subject to: A. The maximum is when x₁ = ₁ X₂ = ₁ S₁ = (Type integers or simplified fractions.) B. There is no maximum. with z = 10x₁ + 12x2 , S₂ = 4x₁ + 2x₂ ≤24 6x₁ + x₂ ≤50 2x₁ + 2x₂ ≤26 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. X₁ ≥ 0, X₂ ≥ 0 and s3 =

An integer programming (maximization) problem was first solved as a linear programming problem, and the objective function value (profit) was $253.67. The two decision variables (X, Y) in the problem had values of X = 12.45 and Y = 32.75. If there is a single optimal solution, which of the following must be true for the optimal integer solution to this problem? 1) X = 12, Y = 322) The objective function value must be less than $253.673) X = 12, Y = 334) The objective function value will be greater than $253.675) The objective function value would still be equal to $253.67

Determine whether the following linear programming problem is infeasible, unbounded, or has multiple optimal solutions. Draw a graph and explain your conclusion.   Maximize 400x + 500y Subject to      2x + 1y > 60                     -3x + 4y < 90                                                 x, y > 0

e. Write out the standard form a standard convex optimization problem and show that the feasible set and the solution set of a standard convex optimization problem are convex.

true/false 1) The objective of the product design and market share optimization problem presented in the textbook is to choose the levels of each product attribute that will maximize the number of sampled customers preferring the brand in question. 2) Dual prices cannot be used for integer programming sensitivity analysis because they are designed for linear programs. 3) generally, The optimal solution to an integer linear program is less sensitive to the constraint coefficients then is a linear program. 4) Multiple choice constraints involve binary variables