Question 1

Solve the following LP problem graphically by enumerating the corner points.
 $$\begin{array} { l l } 
\text { MAX: } & 2 X _ { 1 } + 7 X _ { 2 } \
\text { Subject to: } & 5 X _ { 1 } + 9 X _ { 2 } \leq 90 \
& 9 X _ { 1 } + 8 X _ { 2 } \leq 144 \
& X _ { 2 } \leq 8 \
& X _ { 1 } , X _ { 2 } \geq 0
\end{array}$$

Accepted Answer

Obj = 63.2

Question 2

When the objective function can increase without ever contacting a constraint the LP model is said to be

Accepted Answer

A)  infeasible. 
B)  open ended. 
C)  multi-optimal. 
D)  unbounded. 
A)  infeasible. 
B)  open ended. 
C)  multi-optimal. 
D)  unbounded.

Question 3

The following diagram shows the constraints for a LP model. Assume the point (0,0) satisfies constraint (B,J) but does not satisfy constraints (D,H) or (C,I). Which set of points on this diagram defines the feasible solution space?

Accepted Answer

A)  A, B, E, F, H 
B)  A, D, G, J 
C)  F, G, H, J 
D)  F, G, I, J 
A)  A, B, E, F, H 
B)  A, D, G, J 
C)  F, G, H, J 
D)  F, G, I, J

Question 4

Solve the following LP problem graphically by enumerating the corner points.
 $$\begin{array} { l l } 
\text { MAX: } & 4 X _ { 1 } + 3 X _ { 2 } \
\text { Subject to: } & 6 X _ { 1 } + 7 X _ { 2 } \leq 84 \
& X _ { 1 } \leq 10 \
& X _ { 2 } \leq 8 \
& X _ { 1 } , X _ { 2 } \geq 0
\end{array}$$

Accepted Answer

Obj = 50.2

Question 5

Most individuals manage their individual retirement accounts (IRAs) so they

Accepted Answer

A)  maximize the amount of money they withdraw. 
B)  minimize the amount of taxes they must pay. 
C)  retire with a minimum amount of money. 
D)  leave all their money to the government. 
A)  maximize the amount of money they withdraw. 
B)  minimize the amount of taxes they must pay. 
C)  retire with a minimum amount of money. 
D)  leave all their money to the government.

Question 6

Solve the following LP problem graphically using level curves.
 $$\begin{array} { l l } 
\text { MAX: } & 5 X _ { 1 } + 6 X _ { 2 } \
\text { Subject to: } & 3 X _ { 1 } + 8 X _ { 2 } \leq 48 \
& 12 X _ { 1 } + 11 X _ { 2 } \leq 132 \
& 2 X _ { 1 } + 3 X _ { 2 } \leq 24 \
& X _ { 1 } , X _ { 2 } \geq 0
\end{array}$$

Accepted Answer

Obj = 57.4

Question 7

The following linear programming problem has been written to plan the production of two products. The company wants to maximize its profits. X1 = number of product 1 produced in each batch
X2 = number of product 2 produced in each batch
$$\begin{array} { l l } 
\text { MAX: } & 150 X _ { 1 } + 250 X _ { 2 } \
\text { Subject to: } & 2 X _ { 1 } + 5 X _ { 2 } \leq 200 \
& 3 X _ { 1 } + 7 X _ { 2 } \leq 175 \
& X _ { 1 } , X _ { 2 } \geq 0
\end{array}$$ How much profit is earned if the company produces 10 units of product 1 and 5 units of product 2?

Accepted Answer

A)  750 
B)  2500 
C)  2750 
D)  3250 
A)  750 
B)  2500 
C)  2750 
D)  3250

Question 8

The objective function for a LP model is 3 X1 + 2 X2. If X1 = 20 and X2 = 30, what is the value of the objective function?

Accepted Answer

A)  0 
B)  50 
C)  60 
D)  120 
A)  0 
B)  50 
C)  60 
D)  120

Question 9

The second step in formulating a linear programming problem is

Accepted Answer

A)  Identify any upper or lower bounds on the decision variables. 
B)  State the constraints as linear combinations of the decision variables. 
C)  Understand the problem. 
D)  Identify the decision variables. 
E)  State the objective function as a linear combination of the decision variables. 
A)  Identify any upper or lower bounds on the decision variables. 
B)  State the constraints as linear combinations of the decision variables. 
C)  Understand the problem. 
D)  Identify the decision variables. 
E)  State the objective function as a linear combination of the decision variables.

Question 10

Limited resources are modeled in optimization problems as

Accepted Answer

A)  an objective function. 
B)  constraints. 
C)  decision variables. 
D)  alternatives. 
A)  an objective function. 
B)  constraints. 
C)  decision variables. 
D)  alternatives.

Question 11

Solve the following LP problem graphically using level curves.
 $$\begin{array} { l l } 
\text { MAX: } & 7 X _ { 1 } + 4 X _ { 2 } \
\text { Subject to: } & 2 X _ { 1 } + X _ { 2 } \leq 16 \
& X _ { 1 } + X _ { 2 } \leq 10 \
& 2 X _ { 1 } + 5 X _ { 2 } \leq 40 \
& X _ { 1 } X _ { 2 } \geq 0
\end{array}$$

Accepted Answer

Obj = 58
X

Question 12

A mathematical programming application employed by a shipping company is most likely

Accepted Answer

A)  a product mix problem. 
B)  a manufacturing problem. 
C)  a routing and logistics problem. 
D)  a financial planning problem. 
A)  a product mix problem. 
B)  a manufacturing problem. 
C)  a routing and logistics problem. 
D)  a financial planning problem.

Question 13

Solve the following LP problem graphically by enumerating the corner points.
 MIN: $\quad 8 X _ { 1 } + 3 X _ { 2 }$
Subject to: $\quad X _ { 2 } \geq 8$
$$\begin{array} { l } 
8 \mathrm { X } _ { 1 } + 5 \mathrm { X } _ { 2 } \geq 80 \
3 \mathrm { X } _ { 1 } + 5 \mathrm { X } _ { 2 } \geq 60 \
\mathrm { X } _ { 1 } , \mathrm { X } _ { 2 } \geq 0
\end{array}$$

Accepted Answer

Obj = 48
X

Question 14

If there is no way to simultaneously satisfy all the constraints in an LP model the problem is said to be

Accepted Answer

A)  infeasible. 
B)  open ended. 
C)  multi-optimal. 
D)  unbounded. 
A)  infeasible. 
B)  open ended. 
C)  multi-optimal. 
D)  unbounded.

Question 15

Retail companies try to find

Accepted Answer

A)  the least costly method of transferring goods from warehouses to stores. 
B)  the most costly method of transferring goods from warehouses to stores. 
C)  the largest number of goods to transfer from warehouses to stores. 
D)  the least profitable method of transferring goods from warehouses to stores. 
A)  the least costly method of transferring goods from warehouses to stores. 
B)  the most costly method of transferring goods from warehouses to stores. 
C)  the largest number of goods to transfer from warehouses to stores. 
D)  the least profitable method of transferring goods from warehouses to stores.

Question 16

The symbols X1, Z1, Dog are all examples of

Accepted Answer

A)  decision variables. 
B)  constraints. 
C)  objectives. 
D)  parameters. 
A)  decision variables. 
B)  constraints. 
C)  objectives. 
D)  parameters.

Question 17

This graph shows the feasible region (defined by points ACDEF) and objective function level curve (BG) for a maximization problem. Which point corresponds to the optimal solution to the problem?

Accepted Answer

A)  A 
B)  B 
C)  C 
D)  D 
E)  E 
A)  A 
B)  B 
C)  C 
D)  D 
E)  E

Question 18

Which of the following actions would expand the feasible region of an LP model?

Accepted Answer

A)  Loosening the constraints. 
B)  Tightening the constraints. 
C)  Multiplying each constraint by 2. 
D)  Adding an additional constraint. 
A)  Loosening the constraints. 
B)  Tightening the constraints. 
C)  Multiplying each constraint by 2. 
D)  Adding an additional constraint.

Question 19

The following linear programming problem has been written to plan the production of two products. The company wants to maximize its profits. X1 = number of product 1 produced in each batch
X2 = number of product 2 produced in each batch
$$\begin{array} { l l } 
\text { MAX: } & 150 X _ { 1 } + 250 X _ { 2 } \
\text { Subject to: } & 2 X _ { 1 } + 5 X _ { 2 } \leq 200 \
& 3 X _ { 1 } + 7 X _ { 2 } \leq 175 \
& X _ { 1 } , X _ { 2 } \geq 0
\end{array}$$ How much profit is earned per each unit of product 2 produced?

Accepted Answer

A)  150 
B)  175 
C)  200 
D)  250 
A)  150 
B)  175 
C)  200 
D)  250

Question 20

Bob and Dora Sweet wish to start investing $1,000 each month. The Sweets are looking at five investment plans and wish to maximize their expected return each month. Assume interest rates remain fixed and once their investment plan is selected they do not change their mind. The investment plans offered are:
 Fidelity $\quad 9.1 \%$ return per year
Optima $\quad 16.1 \%$ return per year
CaseWay $\quad 7.3 \%$ return per year
Safeway $\quad 5.6 \%$ return per year
National $\quad 12.3 \%$ return per year Since Optima and National are riskier, the Sweets want a limit of 30% per month of their total investments placed in these two investments. Since Safeway and Fidelity are low risk, they want at least 40% of their investment total placed in these investments.
Formulate the LP model for this problem.

Accepted Answer

The answer of Bob and Dora Sweet wish to start...

Solve the following LP problem graphically by enumerating the corner points. MAX: 2+7 Subject to: 5+9\leq90 9+8\leq144 \leq8 ,\geq0

When the objective function can increase without ever contacting a constraint the LP model is said to be

The following diagram shows the constraints for a LP model. Assume the point (0,0) satisfies constraint (B,J) but does not satisfy constraints (D,H) or (C,I). Which set of points on this diagram defines the feasible solution space?

Solve the following LP problem graphically by enumerating the corner points. MAX: 4+3 Subject to: 6+7\leq84 \leq10 \leq8 ,\geq0

Most individuals manage their individual retirement accounts (IRAs) so they

Solve the following LP problem graphically using level curves. MAX: 5+6 Subject to: 3+8\leq48 12+11\leq132 2+3\leq24 ,\geq0

The objective function for a LP model is 3 X₁ + 2 X₂. If X₁ = 20 and X₂ = 30, what is the value of the objective function?

The second step in formulating a linear programming problem is

Limited resources are modeled in optimization problems as

Solve the following LP problem graphically using level curves. MAX: 7+4 Subject to: 2+\leq16 +\leq10 2+5\leq40 \geq0

A mathematical programming application employed by a shipping company is most likely

Solve the following LP problem graphically by enumerating the corner points. MIN: $\quad 8 X _ { 1 } + 3 X _ { 2 }$ Subject to: $\quad X _ { 2 } \geq 8$ 8+5\geq80 3+5\geq60 ,\geq0

If there is no way to simultaneously satisfy all the constraints in an LP model the problem is said to be

Retail companies try to find

The symbols X₁, Z₁, Dog are all examples of

This graph shows the feasible region (defined by points ACDEF) and objective function level curve (BG) for a maximization problem. Which point corresponds to the optimal solution to the problem?

Which of the following actions would expand the feasible region of an LP model?

Introduction to Modeling and Decision Analysis

Modeling and Solving Lp Problems in a Spreadsheet

Sensitivity Analysis and the Simplex Method

Network Modeling

Integer Linear Programming

Goal Programming and Multiple Objective Optimization

Nonlinear Programming and Evolutionary Optimization

Regression Analysis

Discriminant Analysis

Time Series Forecasting

Introduction to Simulation Using Risk Solver Platform

Queuing Theory

Decision Analysis

Project Management Online

Filters

Exam 2: Introduction to Optimization and Linear Programming

Solve the following LP problem graphically by enumerating the corner points. MAX: 2+7 Subject to: 5+9\leq90 9+8\leq144 \leq8 ,\geq0

When the objective function can increase without ever contacting a constraint the LP model is said to be

The following diagram shows the constraints for a LP model. Assume the point (0,0) satisfies constraint (B,J) but does not satisfy constraints (D,H) or (C,I). Which set of points on this diagram defines the feasible solution space?

Solve the following LP problem graphically by enumerating the corner points. MAX: 4+3 Subject to: 6+7\leq84 \leq10 \leq8 ,\geq0

Most individuals manage their individual retirement accounts (IRAs) so they

Solve the following LP problem graphically using level curves. MAX: 5+6 Subject to: 3+8\leq48 12+11\leq132 2+3\leq24 ,\geq0

The objective function for a LP model is 3 X1 + 2 X2. If X1 = 20 and X2 = 30, what is the value of the objective function?

The second step in formulating a linear programming problem is

Limited resources are modeled in optimization problems as

Solve the following LP problem graphically using level curves. MAX: 7+4 Subject to: 2+\leq16 +\leq10 2+5\leq40 \geq0

A mathematical programming application employed by a shipping company is most likely

Solve the following LP problem graphically by enumerating the corner points. MIN: 8X1+3X2\quad 8 X _ { 1 } + 3 X _ { 2 }8X1​+3X2​ Subject to: X2≥8\quad X _ { 2 } \geq 8X2​≥8 8+5\geq80 3+5\geq60 ,\geq0

If there is no way to simultaneously satisfy all the constraints in an LP model the problem is said to be

Retail companies try to find

The symbols X1, Z1, Dog are all examples of

This graph shows the feasible region (defined by points ACDEF) and objective function level curve (BG) for a maximization problem. Which point corresponds to the optimal solution to the problem?

Which of the following actions would expand the feasible region of an LP model?

Introduction to Modeling and Decision Analysis

Modeling and Solving Lp Problems in a Spreadsheet

Sensitivity Analysis and the Simplex Method

Network Modeling

Integer Linear Programming

Goal Programming and Multiple Objective Optimization

Nonlinear Programming and Evolutionary Optimization

Regression Analysis

Discriminant Analysis

Time Series Forecasting

Introduction to Simulation Using Risk Solver Platform

Queuing Theory

Decision Analysis

Project Management Online

Filters

The objective function for a LP model is 3 X₁ + 2 X₂. If X₁ = 20 and X₂ = 30, what is the value of the objective function?

Solve the following LP problem graphically by enumerating the corner points. MIN: $\quad 8 X _ { 1 } + 3 X _ { 2 }$ Subject to: $\quad X _ { 2 } \geq 8$ 8+5\geq80 3+5\geq60 ,\geq0

The symbols X₁, Z₁, Dog are all examples of