Question 1

What in Excel Solver corresponds to the decision variables in the algebraic model?
A)Optimization Cells
B)Target Cells
C)Changing Cells
D)Decision Cells
E)Parameter Cells

Accepted Answer

In Excel Solver, the decision variables correspond to the changing cells which can be adjusted in order to optimize the target cells. Therefore, the correct answer is option C) Changing Cells.

Question 2

Uhura Enterprises provides consulting services for customers. Consultants are brought in for two-hour shifts. A consultant will spend one full hour with a customer. The customers remain for that hour and then leaves. Each consultant is paid $25 per hour. Let X_i represent the number of consultants starting their shift at hour i, (i = 1,2,3,4). The firm wishes to minimize salary costs while satisfying demand. Customer demand is as follows. 1:00-2:00 4 2:00-3:00 5 3:00-4:00 10 4:00-5:00 4 5:00-6:00 8 Suppose that if consultants start shifts at both 1:00 and 2:00, then the firm will incur an additional fixed cost of $100 (for secretarial support). Let Y be a binary (0-1)variable that equals 1 if this event occurs, and 0 otherwise. Which of the following would "activate" Y variables.) A)X₁ + X₂ ? 5000Y B)X₁ ? 5000Y and X₂ ? 5000Y C)X₁ + X₂ ? 5000Y D)X₁ + X₂ ? Y E)X₁ ? 5000q₁ and X₂ ? 5000q₂ and q₁ + q₂ ? 1 + Y

Accepted Answer

The answer of Uhura Enterprises provides consulting services for customers....

Question 3

When was the Simplex Method developed?
A)1927
B)1937
C)1947
D)1957
E)1967

Accepted Answer

The Simplex Method was developed by George Dantzig in 1947.

Question 4

For an optimization problem a(an)__________________ violates at least one of the constraints.
A)infeasible solution
B)inoptimal solution
C)suboptimal solution
D)unbounded solution
E)simplex solution

Accepted Answer

An infeasible solution is a solution that violates at least one of the constraints, meaning it is not possible to achieve or implement in reality. Therefore, it cannot be considered as a possible solution for the optimization problem.

Question 5

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)(11, 0)
B)(0, 27.5)
C)(0, -40)
D)(9, 5)
E)not enough information is provided to answer the problem

Accepted Answer

To find the optimal solution when constraints (3) and (4) are binding, we need to set them as equations and solve for X and Y.

10X + 4Y = 110
5X - Y = 40

Solving for Y in the second equation: 
Y = 5X - 40

Substituting into the first equation: 
10X + 4(5X-40) = 110 
10X + 20X - 160 = 110 
30X = 270 
X = 9

Substituting X = 9 into Y = 5X - 40: 
Y = 5(9)-40 
Y = 5

Therefore, the optimal solution is (X, Y) = (9, 5).

Question 6

In the "Solver Options" box of Excel Solver, what should be checked to ensure that all decision variables are ≥ 0?
A)Assume Linear Model
B)Use Automatic Scaling
C)Assume Positive
D)Assume Non-Negative
E)Assume Nonzero

Accepted Answer

Choosing "Assume Non-Negative" ensures that all decision variables are set to a minimum value of zero, which is the requirement for linear programming problems. The other options are not relevant to this specific requirement.

Question 7

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

A)bounded and feasible
B)unbounded and feasible
C)bounded and infeasible
D)unbounded and infeasible
E)this is not a Linear Program

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 8

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

A)bounded and feasible
B)unbounded and feasible
C)bounded and infeasible
D)unbounded and infeasible
E)this is not a Linear Program

Accepted Answer

The constraints denote feasible region which is bounded within the limits. The objective function aims to minimize the value of two variables under limitations of constraints. Hence, the given Linear Program is bounded and feasible.

Question 9

Which of the following statements is correct?
A) Given a Linear Program with a maximization objective, the optimal objective function value  may increase if a ? constraint is added to the program.

B) Given a Linear Program with a maximization objective, the optimal objective function value  may increase if a ? constraint is added to the program.

C) Given a Linear Program with a minimization objective, the optimal objective function value cannot increase if a ? constraint is added to the program.

D) Given a Linear Program with a minimization objective, the optimal objective function value cannot increase if a ? constraint is added to the program.

E) Given a Linear Program with a maximization objective, the optimal objective function value may decrease if a ? constraint is added to the program.

Accepted Answer

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

Question 10

If the solution to an optimization problem violates two constraints but satisfies three, it is a(an)________.
A)suboptimal solution
B)infeasible solution
C)inoptimal solution
D)unbounded solution
E)simplex solution

Accepted Answer

An infeasible solution violates one or more constraints and thus cannot be considered a valid solution to the optimization problem. Since the given solution violates two constraints, it is infeasible. A suboptimal solution may not be the best possible solution but it still satisfies all constraints. Inoptimal and simplex solutions are not commonly used terminologies in optimization, and an unbounded solution violates no constraints but can still not be optimal as there are no constraints to restrict it.

Question 11

In the Excel Solver "Add Constraint" box, what two additional choices are available under the relationship operator list besides ≤, ≥, and =?
A)gin and bin
B)int and gin
C)big and int
D)inf and bin
E)int and bin

Accepted Answer

The two additional choices are "int" (integer) and "bin" (binary). "Int" can be used to specify that a decision variable must take on integer values only, while "bin" can be used to specify that a decision variable must take on binary values (0 or 1) only. These additional choices can be helpful in modeling certain types of problems, such as binary or integer programming problems.

Question 12

Uhura Enterprises provides consulting services for customers. Consultants are brought in for two-hour shifts. A consultant will spend one full hour with a customer. The customers remain for that hour and then leave. Each consultant is paid $25 per hour. Let X_i represent the number of consultants starting their shift at hour i, (i = 1,2,3,4). The firm wishes to minimize salary costs while satisfying demand. Customer demand is as follows. 1:00-2:00 $\quad$4 2:00-3:00 $\quad$5 3:00-4:00 $\quad$10 4:00-5:00 $\quad$4 5:00-6:00 $\quad$8 Suppose that two of the customers scheduled to arrive at 1:00 could be rescheduled to arrive at 2:00. Which of the following sets of constraints would allow for this rescheduling option? (In the options below, q and q_i are binary (0-1)variables.) A)X₁ ≥ 4 and X₂ ≥ 5 and X₁ ≥ 2 and X₂ ≥ 7 B)X₁ ≥ 4 and X₂ + X₃ ≥ 15 and X₁ ≥ 2 and X₂ + X₃ ≥ 17 C)50X₁ ≥ 4 and 50X₂ + 50X₃ ≥ 15 and 50X₁ ≥ 2 and 50X₂ + 50X₃ ≥ 17 D)X₁ ≥ 4 - 5000q and X₂ + X₃ ≥ 15 - 5000q and X₁ ≥ 2 -5000(1-q)and X₂ + X₃ ≥ 17 -5000(1-q) E)X₁ ≥ 4 + 5000q and X₂ + X₃ ≥ 15 + 5000q and X₁ ≥ 2 + 5000(1-q) and X₂ + X₃ ≥ 17 + 5000(1-q)

Accepted Answer

The correct answer is D because it allows for the rescheduling of two customers from 1:00 to 2:00 by introducing binary variables q and q_i. When q = 1, the constraints are the same as the original constraints. When q = 0, the constraints allow for two fewer consultants at hour 1 and two more consultants at hour 2.

Question 13

A constraint in Excel Solver consists of what three pieces of information?
A)Target Cell, relationship operator, and Constraint
B)Target Cell, Changing Cells, and Constraint
C)Cell Reference, relationship operator, and Constraint
D)Cell Reference, Changing Cells, and Constraint
E)Target Cell, Changing Cells, and Cell Reference

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 14

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? A)none of the functions is linear B)all three functions are linear C)h is linear, but g and i are not linear D)i is linear, but g and h are not linear E)h and i are linear, but g is not linear

Accepted Answer

A function is linear if it satisfies two properties: 
1) Homogeneity: Scaling the inputs scales the output proportionally.
2) Additivity: The function of the sum of two inputs is equal to the sum of the function of the individual inputs.

g(x, y) = 4x - 9y is not linear because it fails the homogeneity property (scaling the inputs results in a non-proportional scaling of the output).
h(x, y, z) =13x+ y + 3z - 6 satisfies both properties and therefore is linear.
i(y, z) = z - y satisfies both properties and is also linear.

Therefore, the correct answer is E, h and i are linear, but g is not linear.

Question 15

George Dantzig developed the ___________________ in 1947 to solve Linear Programs.
A)Complex Method
B)Multiplex Method
C)Simplex Method
D)Superplex Method
E)Perplex Method

Accepted Answer

The Simplex Method is the correct choice, as it was developed in 1947 by George Dantzig specifically to solve Linear Programs. The other answer choices are either not related to Linear Programming or were not developed by Dantzig.

Question 16

The two primary Excel tools for diagnosing problems in models are ___________________.
A)Error Auditing and Formula Checking
B)Error Auditing and Formula Auditing
C)Error Checking and Formula Auditing
D)Error Checking and Formula Checking
E)Error Diagnosing and Formula Debugging

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 17

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)?
A)(0, 20)
B)(20, 0)
C)(10, 10)
D)(0, 14)
E)(35, 0)

Accepted Answer

When constraints (3) and (4) are binding, we need to find the intersection point of the lines. 
From constraint (3): X + Y = 20, when X = 0, Y = 20 and when Y = 0, X = 20.
From constraint (4): 2X + 5Y = 70, when X = 0, Y = 14 and when Y = 0, X = 35/2.
The intersection point is where x = 10 and y = 10. Therefore, the optimal solution is (10, 10).

Question 18

What in Excel Solver corresponds to the objective function in the algebraic model?
A)Optimization Cell
B)Target Cell
C)Changing Cell
D)Constraint Cell
E)Parameter Cell

Accepted Answer

The Target Cell in Excel Solver corresponds to the objective function in the algebraic model. This is the cell that we want to optimize or maximize/minimize.

Question 19

Which Excel tool provides solutions to Linear Programs?
A)Solver
B)Answer
C)Simplexer
D)Computer
E)Goal Seek

Accepted Answer

Solver is an Excel add-in that can be used to solve optimization problems, including linear programming. Solver uses a method called Linear Programming (LP) which is one of the most frequently used methods in optimization problems. Therefore, the best choice is A: Solver.

Question 20

Consider the Linear Program below. Which of the choices represents the best (tightest)lower bound? 
Max 2X + Y
Subject to
X + Y ? 10
X, Y ? 0

A)(?, -?)
B)(-?, -?)
C)(0, 0)
D)(5, 0)
E)(25, 16)

Accepted Answer

The feasible region is the triangle bounded by the x and y axes and the line $x+y=10$.

To find the best lower bound, we need to find the minimum value of the objective function 2X + Y within this feasible region.

We see that the objective function is minimized at the corner point (5,5). Thus, the minimum value of the objective function is 2(5) + 5 = 15.

Since this is a maximization problem, any lower bound on the objective function must be less than or equal to 15.

The choice (5, 0) represents the best (tightest) lower bound of 10, since it is the value of the objective function at the point (5,0) in the feasible region, and 10 is less than the minimum value of 15.

Therefore, the answer is D.

Quiz 17: Spreadsheet Modeling: an Introduction

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

When was the Simplex Method developed?

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

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) ?

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

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

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

Which of the following statements is correct?

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

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

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

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?

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

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

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) ?

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

Which Excel tool provides solutions to Linear Programs?

Consider the Linear Program below. Which of the choices represents the best (tightest) lower bound? Max 2X + Y Subject to X + Y ? 10 X, Y ? 0