Question 1

How can the following Linear Program be characterized?
Min X + 2Y
Subject to
X ≤ 20
X, Y ≥ -40

Accepted Answer

The given Linear Program is unbounded and feasible because there are no constraints limiting the value of Y to a maximum, allowing the objective function to decrease indefinitely by increasing Y. However, it is feasible because there exist values of X and Y that satisfy all the constraints.

Question 2

George Dantzig developed the ___________________ in 1947 to solve Linear Programs.

Accepted Answer

George Dantzig developed the Simplex Method in 1947, which revolutionized the field of optimization and made it possible to solve larger and more complex linear programming problems.

Question 3

Consider the following constraints from a two-variable Linear Program.
(1) X ≥ 0
(2) Y ≥ 0
(3) 10X + 4Y ≤ 110
(4) 5X - Y ≤ 40
If constraints (3) and (4) are binding, what is the optimal solution (X, Y)?

Accepted Answer

Since constraints (3) and (4) are binding, we can rewrite them as equalities:
10X + 4Y = 110
5X - Y = 40
Solving these two equations simultaneously gives X = 9 and Y = 5, which satisfies the non-negativity constraints (1) and (2). Therefore, the optimal solution is (9, 5).

Question 4

A constraint in Excel Solver consists of what three pieces of information?

Accepted Answer

A constraint in Excel Solver is defined by a Cell Reference (which cell or cells are being constrained), a relationship operator (such as <=, >=, =), and a Constraint value or reference (the specific condition or value that the referenced cell(s) must meet).

Question 5

When was the Simplex Method developed?

Accepted Answer

The Simplex Method was developed by George Dantzig in 1947.

Question 6

In the "Solver Options" box of Excel Solver, what should be checked to ensure that the Simplex Method is used to solve the model?

Accepted Answer

The Simplex Method is used for linear programming problems, so checking "Assume Linear Model" ensures that Excel Solver uses the Simplex Method.

Question 7

Consider the following constraints from a two-variable Linear Program.
(1) X ≥ 0
(2) Y ≥ 0
(3) X + Y ≤ 20
(4) 2X + 5Y ≤ 70
If constraints (3) and (4) are binding, what is the optimal solution (X, Y)?

Accepted Answer

Constraints (3) and (4) are binding, which means they hold with equality at the optimal solution. Solving for (3) and (4) simultaneously, we get X=10 and Y=10, which satisfies constraints (1) and (2) as well. Therefore, the optimal solution is (10, 10) and the correct answer is choice C.

Question 8

Consider the following three functions: G(x, y) = 4x - 9y² H(x, y, z) = 13x + y + 3z -6 I(y, z) = z - y Which of the following is true regarding the linearity of the functions?

Accepted Answer

A function is linear if it satisfies two properties: 
1. Homogeneity: f(cx, cy) = c f(x, y)
2. Additivity: f(x1 + x2 , y1 + y2) = f(x1, y1) + f(x2, y2)

G(x, y) is not homogeneous as G(cx, cy) = 4cx - 9cy ≠ c(4x - 9y) = cG(x, y). Therefore, G(x, y) is not linear.
H(x, y, z) and I(y, z) are both homogeneous and additive. Therefore, H(x, y, z) and I(y, z) are linear.

Question 9

Which Excel tool provides solutions to Linear Programs?

Accepted Answer

Solver is the tool within Excel that provides solutions to Linear Programs. It uses algorithms such as the simplex method to optimize linear objectives subject to linear constraints. Option B, "Answer," is not a tool within Excel. Option C, "Simplexer," is not a commonly used term for Linear Programming solvers. Option D, "Computer," is too broad and doesn't specify which tool or software would provide the solutions. Option E, "Goal Seek," is a tool that allows you to set a specific cell value by adjusting another cell value, but is not intended for solving LP problems.

Question 10

Which of the following statements is correct?

Accepted Answer

The answer of Which of the following statements is correct?
...

Question 11

Constraints at their limits at the optimal solution of a Linear Program, that is, with the left-hand-side value equal to the right-hand-side value, are called _________________________.

Accepted Answer

Constraints that are at their limits at the optimal solution of a Linear Program are called binding constraints because they restrict the feasible region and affect the optimal solution. Non-binding constraints do not affect the optimal solution, while equality constraints have a fixed value that must be satisfied at all times. Limiting constraints and synergistic constraints are not commonly used terms in Linear Programming.

Question 12

What in Excel Solver corresponds to the decision variables in the algebraic model?

Accepted Answer

The changing cells in Excel Solver correspond to the decision variables in the algebraic model. These are the cells for which we want to find the optimal values.

Question 13

In the "Solver Options" box of Excel Solver, what should be checked to ensure that all decision variables are ≥ 0?

Accepted Answer

The option that should be checked to ensure that all decision variables are ≥ 0 is the "Assume Non-Negative" option. This will instruct Solver to only consider solutions where all decision variables have values that are equal to or greater than zero.

Question 14

What in Excel Solver corresponds to the objective function in the algebraic model?

Accepted Answer

The target cell in Excel Solver corresponds to the objective function in the algebraic model. The objective function is the equation that we aim to optimize, and the target cell is the cell that contains the formula for the objective function in Excel Solver.

Question 15

The two primary Excel tools for diagnosing problems in models are ___________________.

Accepted Answer

The two primary Excel tools for diagnosing problems in models are Error Checking and Formula Auditing. Error Checking identifies and highlights any errors in the formula, while Formula Auditing visually traces the precedent or dependent cells for the selected cell or formula to check if there are any errors. Therefore, the answer is C - Error Checking and Formula Auditing.

Question 16

In the Excel Solver "Add Constraint" box, what two additional choices are available under the relationship operator list besides ≤, ≥, and =?

Accepted Answer

The two additional choices available in the relationship operator list are "int" (integer) and "bin" (binary). These options allow for constraints to be placed on specific types of variables, such as requiring a variable to be a whole number (integer) or allowing it to only take on values of zero or one (binary).

Question 17

If the solution to an optimization problem violates two constraints but satisfies three, it is a(an) ________.

Accepted Answer

If the solution violates two constraints, then it does not meet all the requirements of the problem and is therefore infeasible. A suboptimal solution would satisfy all constraints but would not be the best possible solution. An inoptimal solution is not a commonly used term in optimization. An unbounded solution arises when the objective function can be infinitely improved, and a simplex solution refers to a specific algorithm used to solve linear programming problems.

Question 18

In the "Solver Parameters" box of Excel Solver, what is clicked to actually solve the problem?

Accepted Answer

"SOLVE" is clicked to actually solve the problem.

Question 19

For an optimization problem a(an) __________________ violates at least one of the constraints.

Accepted Answer

An infeasible solution violates at least one of the constraints, making it impossible to achieve. Therefore, A is the best choice for this question. The other options, B through E, do not necessarily violate any constraints: a suboptimal solution may meet all the constraints but be less than optimal, an unbounded solution means there is no limit to the objective function within the constraints, and a simplex solution refers to the algorithm used to solve linear programming problems.

Question 20

How can the following Linear Program be characterized?
Min X + 2Y
Subject to
X ≤ 20
Y ≤ 5
X, Y ≥ -40

Accepted Answer

The feasible region is a rectangle with vertices (-40,-40), (-40,5), (20,-40), and (20,5). Since the objective function is a linear function, it attains its minimum value at one of the vertices of the feasible region. Therefore, the optimal solution must occur at one of the vertices of the feasible region. Since the feasible region is bounded and there are only a finite number of vertices, the problem is both bounded and feasible.

Quiz 18: Introduction to Optimization

How can the following Linear Program be characterized? Min X + 2Y Subject to X ≤ 20 X, Y ≥ -40

George Dantzig developed the ___________________ in 1947 to solve Linear Programs.

Consider the following constraints from a two-variable Linear Program. (1) X ≥ 0 (2) Y ≥ 0 (3) 10X + 4Y ≤ 110 (4) 5X - Y ≤ 40 If constraints (3) and (4) are binding, what is the optimal solution (X, Y) ?

A constraint in Excel Solver consists of what three pieces of information?

When was the Simplex Method developed?

In the "Solver Options" box of Excel Solver, what should be checked to ensure that the Simplex Method is used to solve the model?

Consider the following constraints from a two-variable Linear Program. (1) X ≥ 0 (2) Y ≥ 0 (3) X + Y ≤ 20 (4) 2X + 5Y ≤ 70 If constraints (3) and (4) are binding, what is the optimal solution (X, Y) ?

Consider the following three functions: G(x, y) = 4x - 9y² H(x, y, z) = 13x + y + 3z -6 I(y, z) = z - y Which of the following is true regarding the linearity of the functions?

Which Excel tool provides solutions to Linear Programs?

Which of the following statements is correct?

Constraints at their limits at the optimal solution of a Linear Program, that is, with the left-hand-side value equal to the right-hand-side value, are called _________________________.

What in Excel Solver corresponds to the decision variables in the algebraic model?

In the "Solver Options" box of Excel Solver, what should be checked to ensure that all decision variables are ≥ 0?

What in Excel Solver corresponds to the objective function in the algebraic model?

The two primary Excel tools for diagnosing problems in models are ___________________.

In the Excel Solver "Add Constraint" box, what two additional choices are available under the relationship operator list besides ≤, ≥, and =?

If the solution to an optimization problem violates two constraints but satisfies three, it is a(an) ________.

In the "Solver Parameters" box of Excel Solver, what is clicked to actually solve the problem?

For an optimization problem a(an) __________________ violates at least one of the constraints.

How can the following Linear Program be characterized? Min X + 2Y Subject to X ≤ 20 Y ≤ 5 X, Y ≥ -40

Quiz 18: Introduction to Optimization

How can the following Linear Program be characterized? Min X + 2Y Subject to X ≤ 20 X, Y ≥ -40

George Dantzig developed the ___________________ in 1947 to solve Linear Programs.

Consider the following constraints from a two-variable Linear Program. (1) X ≥ 0 (2) Y ≥ 0 (3) 10X + 4Y ≤ 110 (4) 5X - Y ≤ 40 If constraints (3) and (4) are binding, what is the optimal solution (X, Y) ?

A constraint in Excel Solver consists of what three pieces of information?

When was the Simplex Method developed?

In the "Solver Options" box of Excel Solver, what should be checked to ensure that the Simplex Method is used to solve the model?

Consider the following constraints from a two-variable Linear Program. (1) X ≥ 0 (2) Y ≥ 0 (3) X + Y ≤ 20 (4) 2X + 5Y ≤ 70 If constraints (3) and (4) are binding, what is the optimal solution (X, Y) ?

Consider the following three functions: G(x, y) = 4x - 9y2 H(x, y, z) = 13x + y + 3z -6 I(y, z) = z - y Which of the following is true regarding the linearity of the functions?

Which Excel tool provides solutions to Linear Programs?

Which of the following statements is correct?

Constraints at their limits at the optimal solution of a Linear Program, that is, with the left-hand-side value equal to the right-hand-side value, are called _________________________.

What in Excel Solver corresponds to the decision variables in the algebraic model?

In the "Solver Options" box of Excel Solver, what should be checked to ensure that all decision variables are ≥ 0?

What in Excel Solver corresponds to the objective function in the algebraic model?

The two primary Excel tools for diagnosing problems in models are ___________________.

In the Excel Solver "Add Constraint" box, what two additional choices are available under the relationship operator list besides ≤, ≥, and =?

If the solution to an optimization problem violates two constraints but satisfies three, it is a(an) ________.

In the "Solver Parameters" box of Excel Solver, what is clicked to actually solve the problem?

For an optimization problem a(an) __________________ violates at least one of the constraints.

How can the following Linear Program be characterized? Min X + 2Y Subject to X ≤ 20 Y ≤ 5 X, Y ≥ -40

Consider the following three functions: G(x, y) = 4x - 9y² H(x, y, z) = 13x + y + 3z -6 I(y, z) = z - y Which of the following is true regarding the linearity of the functions?