Question 1

In using the Solver package to solve a linear programming problem, the objective function expression and its value are defined in the

Accepted Answer

A)  target cell/s 
B)  changing cell/s 
C)  constraint cells 
D)  variable cells 
A)  target cell/s 
B)  changing cell/s 
C)  constraint cells 
D)  variable cells

Question 2

Problem $\mathrm{A}$ is a given formulation of a linear program with an optimal solution and exactly one equality constraint. Problem B is a formulation obtained from Problem A by replacing the equality constraint with a pair of inequality constraints obtained by serially replacing the equality sign of the constraint with $\pounds$ and ${ }^{3}$ signs, leaving all other things unchanged. Problems A and B will have

Accepted Answer

A)  the same optimal solution and same objective function value 
B)  the same optimal solution but different objective function values 
C)  different optimal solutions but same objective function value 
D)  different optimal solutions and different objective function values 
E)  same or different solution profile depending on the role of the constraints in the solutions 
A)  the same optimal solution and same objective function value 
B)  the same optimal solution but different objective function values 
C)  different optimal solutions but same objective function value 
D)  different optimal solutions and different objective function values 
E)  same or different solution profile depending on the role of the constraints in the solutions

Question 3

Problem $A$ is a given formulation of a linear program with an optimal solution. Problem $B$ is a formulation obtained by adding a constant to the right hand side of Constraint 1 of Problem A and leaving all other things unchanged. Problems A and B will have

Accepted Answer

A)  the same optimal solution and same objective function value 
B)  the same optimal solution but different objective function values 
C)  different optimal solutions but same objective function value 
D)  different optimal solutions and different objective function values 
E)  same or different solution profile depending on the role of the constraint in the solutions 
A)  the same optimal solution and same objective function value 
B)  the same optimal solution but different objective function values 
C)  different optimal solutions but same objective function value 
D)  different optimal solutions and different objective function values 
E)  same or different solution profile depending on the role of the constraint in the solutions

Question 4

Problem $A$ is a given formulation of a linear program with an optimal solution. Problem $B$ is a formulation obtained by adding a constant to the objective function of Problem A and leaving all other things unchanged. Problems A and B will have

Accepted Answer

A)  the same optimal solution and same objective function value 
B)  the same optimal solution but different objective function values 
C)  different optimal solutions but same objective function value 
D)  different optimal solutions and different objective function values 
E)  same or different solution profile depending on the role of the constraint in the solutions 
A)  the same optimal solution and same objective function value 
B)  the same optimal solution but different objective function values 
C)  different optimal solutions but same objective function value 
D)  different optimal solutions and different objective function values 
E)  same or different solution profile depending on the role of the constraint in the solutions

Question 5

A linear programming formulation, which has an optimal solution, can become unbounded by removal of a single constraint.

Accepted Answer

A) True 
 B)False

Question 6

Problem $A$ is a given formulation of a linear program with an optimal solution. Problem B is a formulation obtained from Problem A by adding a constraint, and leaving all other things unchanged. Problems A and B will have

Accepted Answer

A)  the same optimal solution and same objective function value 
B)  the same optimal solution but different objective function values 
C)  different optimal solutions but same objective function value 
D)  different optimal solutions and different objective function values 
E)  same or different solution profile depending on the role of the constraint in Problem B 
A)  the same optimal solution and same objective function value 
B)  the same optimal solution but different objective function values 
C)  different optimal solutions but same objective function value 
D)  different optimal solutions and different objective function values 
E)  same or different solution profile depending on the role of the constraint in Problem B

Question 7

Problem $\mathrm{A}$ is a given formulation of a linear program with an optimal solution. Problem $\mathrm{B}$ is a formulation obtained from Problem A by omitting constraint 1 of Problem A and leaving all other things unchanged. Problems A and B will have

Accepted Answer

A)  the same optimal solution and same objective function value 
B)  the same optimal solution but different objective function values 
C)  different optimal solutions but same objective function value 
D)  different optimal solutions and different objective function values 
E)  same or different solution profile depending on the role of the constraints in the solutions 
A)  the same optimal solution and same objective function value 
B)  the same optimal solution but different objective function values 
C)  different optimal solutions but same objective function value 
D)  different optimal solutions and different objective function values 
E)  same or different solution profile depending on the role of the constraints in the solutions

Question 8

Problem A is a given formulation of a linear program with an optimal solution. Problem B is a formulation obtained from Problem A by adding a redundant constraint, leaving all other things unchanged. Problems A and B will have

Accepted Answer

A)  the same optimal solution and same objective function value 
B)  the same optimal solution but different objective function values 
C)  different optimal solutions but same objective function value 
D)  different optimal solutions and different objective function values 
E)  same or different solution profile depending on the role of the constraints in the solutions 
A)  the same optimal solution and same objective function value 
B)  the same optimal solution but different objective function values 
C)  different optimal solutions but same objective function value 
D)  different optimal solutions and different objective function values 
E)  same or different solution profile depending on the role of the constraints in the solutions

Question 9

Midwest Money Manger (MMM), an investment firm, has $\$ 4$ million to invest. They have four choices, namely stocks, bonds, money-markets and government securities. The respective projected yields are: $15 \%, 9 \%, 6 \%$, and $4.5 \%$. The respective risk indices are: $0.2,0.11,0.07$, and 0.01 . They can also put their money in a vault (safe deposit vault), earning $0 \%$ and having a risk index of 0 . It is assumed that the risk index of a portfolio is equal to the weighted average value of the individual index, using the proportion of investment as weights. MMM wants to limit its investment in stocks and bonds to a maximum of $50 \%$ of the total investment. Investment in money markets should always be less than or equal to investment in government securities. MMM wants to earn at least $\$ 80,000$ in the next year and minimize the risk of its portfolio. Formulate this as a linear program. Specify the decision variables, constraints, and the objective function.

Accepted Answer

Decision variables:
Let @#LAT-DLM& be the number o

Question 10

A linear programming formulation, which has a unique optimal solution, can be unbounded for a different objective function.

Accepted Answer

A) True 
 B)False

Question 11

A two-variable linear programming problem can only be solved by the simplex method.

Accepted Answer

A) True 
 B)False

Question 12

A linear programming formulation, which has an optimal solution, cannot become unbounded by the addition of a single constraint.

Accepted Answer

A) True 
 B)False

Question 13

Problem $A$ is a given formulation of a linear program with an optimal solution. Problem $B$ is a formulation obtained by multiplying all constraints of Problem A by a positive constant and leaving all other things unchanged. Problems A and B will have

Accepted Answer

A)  the same optimal solution and same objective function value 
B)  the same optimal solution but different objective function values 
C)  different optimal solutions but same objective function value 
D)  different optimal solutions and different objective function values 
E)  same or different solution profile depending on the role of the constraint in the solutions 
A)  the same optimal solution and same objective function value 
B)  the same optimal solution but different objective function values 
C)  different optimal solutions but same objective function value 
D)  different optimal solutions and different objective function values 
E)  same or different solution profile depending on the role of the constraint in the solutions

Question 14

A linear programming formulation, which is unbounded, may become bounded and have an optimal solution by the addition of a constraint.

Accepted Answer

A) True 
 B)False

Question 15

In a linear program, if a constraint simply relates the ratio of linear expressions involving decision variables to another decision variable through $=, \geq$, or $\leq$, then the constraint can always be converted to a linear constraint.

Accepted Answer

A) True 
 B)False

Question 16

In a linear program, if a constraint simply relates the ratio of linear expressions involving decision variables to a constant through $=$, $\geq$, or $\leq$, then the constraint can always be converted to a linear constraint.

Accepted Answer

A) True 
 B)False

Question 17

If the sale of the first 10 units of a product gives a profit of $\$ 10.00$ per unit and every additional unit sold gives a profit of $\$ 15.00$ per unit, the situation cannot be modeled easily as a linear program.

Accepted Answer

A) True 
 B)False

Question 18

In a linear program, if a constraint simply relates the ratio of constant multiples of two decision variables to a constant through $=, \geq$, or $\leq$, then the constraint can always be converted to a linear constraint.

Accepted Answer

A) True 
 B)False

Question 19

Midwest Money Manger (MMM), an investment firm, has $\$ 4$ million to invest. They have four choices, namely stocks, bonds, money-markets, and government securities. The respective projected yields are: $15 \%, 9 \%, 6 \%$, and $4.5 \%$. The respective risk indices are: $0.2,0.11,0.07$, and 0.01 . It is assumed that risk index of a portfolio is equal to the weighted average value of individual index, using the proportion of investment as weights. MMM wants to limit its investment in stocks and bonds to a maximum of $50 \%$ of the total investment. Investment in money markets should always be less than or equal to investment in government securities. MMM wants to earn at least $\$ 400,000$ in the next year and minimize the risk of its portfolio. Formulate this as a linear program. Specify the decision variables, constraints, and the objective function.

Accepted Answer

Decision variables:
Let @#LAT-DLM& be the number o

Question 20

In formulating a coffee blending problem where there are three types of coffee beans, the objective is to find a recipe to make 1 pound of blended coffee that satisfies a set of properties at the least cost. The decision variables are $X_{1}, X_{2}$, and ${ }^{X_{3}}$, representing pounds (actually fractional pounds) of coffee beans used per pound of blended coffee. Suppose that bitterness is a property measured as an index from 1 to 6 and a blend's bitterness is given by the weighted average (using the weight fraction of each beans in the blend as the weight) of the bitterness of individual beans going into the blend. Suppose that the bitterness indices for the three beans are respectively 2, 4, and 5 . A blend with bitterness in the range 3 to 4.5 is most desirable. The appropriate constraint/s will be

Accepted Answer

A)  $2 X_{1}+4 X_{2}+5 X_{3} \geq 3.0$ 
B)  $2 X_{1}+4 X_{2}+5 X_{3} \leq 4.5$ 
C)  $2 X_{1}+4 X_{2}+5 X_{3} \geq 3.0$ and $2 X_{1}+4 X_{2}+5 X_{3} \leq 4.5$ 
D)  the constraint/s are not correct since weights are not correctly represented 
A)  $2 X_{1}+4 X_{2}+5 X_{3} \geq 3.0$ 
B)  $2 X_{1}+4 X_{2}+5 X_{3} \leq 4.5$ 
C)  $2 X_{1}+4 X_{2}+5 X_{3} \geq 3.0$ and $2 X_{1}+4 X_{2}+5 X_{3} \leq 4.5$ 
D)  the constraint/s are not correct since weights are not correctly represented

In using the Solver package to solve a linear programming problem, the objective function expression and its value are defined in the

Problem $A$ is a given formulation of a linear program with an optimal solution. Problem $B$ is a formulation obtained by adding a constant to the right hand side of Constraint 1 of Problem A and leaving all other things unchanged. Problems A and B will have

Problem $A$ is a given formulation of a linear program with an optimal solution. Problem $B$ is a formulation obtained by adding a constant to the objective function of Problem A and leaving all other things unchanged. Problems A and B will have

A linear programming formulation, which has an optimal solution, can become unbounded by removal of a single constraint.

Problem $A$ is a given formulation of a linear program with an optimal solution. Problem B is a formulation obtained from Problem A by adding a constraint, and leaving all other things unchanged. Problems A and B will have

Problem $\mathrm{A}$ is a given formulation of a linear program with an optimal solution. Problem $\mathrm{B}$ is a formulation obtained from Problem A by omitting constraint 1 of Problem A and leaving all other things unchanged. Problems A and B will have

Problem A is a given formulation of a linear program with an optimal solution. Problem B is a formulation obtained from Problem A by adding a redundant constraint, leaving all other things unchanged. Problems A and B will have

A linear programming formulation, which has a unique optimal solution, can be unbounded for a different objective function.

A two-variable linear programming problem can only be solved by the simplex method.

A linear programming formulation, which has an optimal solution, cannot become unbounded by the addition of a single constraint.

Problem $A$ is a given formulation of a linear program with an optimal solution. Problem $B$ is a formulation obtained by multiplying all constraints of Problem A by a positive constant and leaving all other things unchanged. Problems A and B will have

A linear programming formulation, which is unbounded, may become bounded and have an optimal solution by the addition of a constraint.

In a linear program, if a constraint simply relates the ratio of linear expressions involving decision variables to another decision variable through $=, \geq$ , or $\leq$ , then the constraint can always be converted to a linear constraint.

In a linear program, if a constraint simply relates the ratio of linear expressions involving decision variables to a constant through $=$ , $\geq$ , or $\leq$ , then the constraint can always be converted to a linear constraint.

If the sale of the first 10 units of a product gives a profit of $\$ 10.00$ per unit and every additional unit sold gives a profit of $\$ 15.00$ per unit, the situation cannot be modeled easily as a linear program.

In a linear program, if a constraint simply relates the ratio of constant multiples of two decision variables to a constant through $=, \geq$ , or $\leq$ , then the constraint can always be converted to a linear constraint.

Introduction to Management Science, Modeling, and Excel Spreadsheets

Forecasting

Linear Programming: Basic Concepts and Graphical Solutions

Linear Programming: Sensitivity Analysis, Duality, and Specialized Models

Transportation, Assignment, and Transshipment Problems

Integer Programming

Network Optimization Models

Nonlinear Optimization Models

Multi-Criteria Models

Decision Theory

Markov Analysis

Waiting Line Models

Simulation Cdrom Modules

Filters

Exam 4: Linear Programming: Applications and Solutions

In using the Solver package to solve a linear programming problem, the objective function expression and its value are defined in the

Problem AAA is a given formulation of a linear program with an optimal solution. Problem BBB is a formulation obtained by adding a constant to the right hand side of Constraint 1 of Problem A and leaving all other things unchanged. Problems A and B will have

Problem AAA is a given formulation of a linear program with an optimal solution. Problem BBB is a formulation obtained by adding a constant to the objective function of Problem A and leaving all other things unchanged. Problems A and B will have

A linear programming formulation, which has an optimal solution, can become unbounded by removal of a single constraint.

Problem AAA is a given formulation of a linear program with an optimal solution. Problem B is a formulation obtained from Problem A by adding a constraint, and leaving all other things unchanged. Problems A and B will have

Problem A\mathrm{A}A is a given formulation of a linear program with an optimal solution. Problem B\mathrm{B}B is a formulation obtained from Problem A by omitting constraint 1 of Problem A and leaving all other things unchanged. Problems A and B will have

Problem A is a given formulation of a linear program with an optimal solution. Problem B is a formulation obtained from Problem A by adding a redundant constraint, leaving all other things unchanged. Problems A and B will have

A linear programming formulation, which has a unique optimal solution, can be unbounded for a different objective function.

A two-variable linear programming problem can only be solved by the simplex method.

A linear programming formulation, which has an optimal solution, cannot become unbounded by the addition of a single constraint.

Problem AAA is a given formulation of a linear program with an optimal solution. Problem BBB is a formulation obtained by multiplying all constraints of Problem A by a positive constant and leaving all other things unchanged. Problems A and B will have

A linear programming formulation, which is unbounded, may become bounded and have an optimal solution by the addition of a constraint.

In a linear program, if a constraint simply relates the ratio of linear expressions involving decision variables to another decision variable through =,≥=, \geq=,≥ , or ≤\leq≤ , then the constraint can always be converted to a linear constraint.

In a linear program, if a constraint simply relates the ratio of linear expressions involving decision variables to a constant through === , ≥\geq≥ , or ≤\leq≤ , then the constraint can always be converted to a linear constraint.

If the sale of the first 10 units of a product gives a profit of $10.00\$ 10.00$10.00 per unit and every additional unit sold gives a profit of $15.00\$ 15.00$15.00 per unit, the situation cannot be modeled easily as a linear program.

In a linear program, if a constraint simply relates the ratio of constant multiples of two decision variables to a constant through =,≥=, \geq=,≥ , or ≤\leq≤ , then the constraint can always be converted to a linear constraint.

Introduction to Management Science, Modeling, and Excel Spreadsheets

Forecasting

Linear Programming: Basic Concepts and Graphical Solutions

Linear Programming: Sensitivity Analysis, Duality, and Specialized Models

Transportation, Assignment, and Transshipment Problems

Integer Programming

Network Optimization Models

Nonlinear Optimization Models

Multi-Criteria Models

Decision Theory

Markov Analysis

Waiting Line Models

Simulation Cdrom Modules

Filters

Problem $A$ is a given formulation of a linear program with an optimal solution. Problem $B$ is a formulation obtained by adding a constant to the right hand side of Constraint 1 of Problem A and leaving all other things unchanged. Problems A and B will have

Problem $A$ is a given formulation of a linear program with an optimal solution. Problem $B$ is a formulation obtained by adding a constant to the objective function of Problem A and leaving all other things unchanged. Problems A and B will have

Problem $A$ is a given formulation of a linear program with an optimal solution. Problem B is a formulation obtained from Problem A by adding a constraint, and leaving all other things unchanged. Problems A and B will have

Problem $\mathrm{A}$ is a given formulation of a linear program with an optimal solution. Problem $\mathrm{B}$ is a formulation obtained from Problem A by omitting constraint 1 of Problem A and leaving all other things unchanged. Problems A and B will have

Problem $A$ is a given formulation of a linear program with an optimal solution. Problem $B$ is a formulation obtained by multiplying all constraints of Problem A by a positive constant and leaving all other things unchanged. Problems A and B will have

In a linear program, if a constraint simply relates the ratio of linear expressions involving decision variables to another decision variable through $=, \geq$ , or $\leq$ , then the constraint can always be converted to a linear constraint.

In a linear program, if a constraint simply relates the ratio of linear expressions involving decision variables to a constant through $=$ , $\geq$ , or $\leq$ , then the constraint can always be converted to a linear constraint.

If the sale of the first 10 units of a product gives a profit of $\$ 10.00$ per unit and every additional unit sold gives a profit of $\$ 15.00$ per unit, the situation cannot be modeled easily as a linear program.

In a linear program, if a constraint simply relates the ratio of constant multiples of two decision variables to a constant through $=, \geq$ , or $\leq$ , then the constraint can always be converted to a linear constraint.