Question 1

For the line that has the equation 4X1 + 8X2 = 88,an axis intercept is

Accepted Answer

A)  (0, 22). 
B)  (6, 0). 
C)  (6, 22). 
D)  (0, 11). 
A)  (0, 22). 
B)  (6, 0). 
C)  (6, 22). 
D)  (0, 11).

Question 2

A modeler is limited to two or fewer decision variables when using the ________.

Accepted Answer

The answer of A modeler is limited to two or...

Question 3

The graphical method is a practical method for solving product mix problems of any size,provided the decision maker has sufficient quantities of graph paper.

Accepted Answer

A) True 
 B)False

Question 4

A parameter is a region that represents all permissible combinations of the decision variables in a linear programming model.

Accepted Answer

A) True 
 B)False

Question 5

What are the assumptions of linear programming? Provide examples of each.

Accepted Answer

The assumptions are certainty,linearity,

Question 6

Only corner points should be considered for the optimal solution to a linear programming problem.

Accepted Answer

A) True 
 B)False

Question 7

The ________ is an expression in linear programming models that states mathematically what is being maximized or minimized.

Accepted Answer

The answer of The ________ is an expression in linear...

Question 8

A manager is interested in deciding production quantities for products A,B,and C.He has an inventory of 20 tons each of raw materials 1,2,3,and 4 that are used in the production of products A,B,and C.He can further assume that he can sell all of what he makes.Which of the following statements is correct?

Accepted Answer

A)  The manager has four decision variables. 
B)  The manager has three constraints. 
C)  The manager has three decision variables. 
D)  The manager can solve this problem graphically. 
A)  The manager has four decision variables. 
B)  The manager has three constraints. 
C)  The manager has three decision variables. 
D)  The manager can solve this problem graphically.

Question 9

While glancing over the sensitivity report,you note that the stitching labor has a shadow price of $10 and a lower limit of 24 hours with an upper limit of 36 hours.If your original right hand value for stitching labor was 30 hours,you know that

Accepted Answer

A)  the next worker that offers to work an extra 8 hours should receive at least $80. 
B)  you can send someone home 6 hours early and still pay them the $60 they would have earned while on the clock. 
C)  you would be willing pay up to $60 for someone to work another 6 hours. 
D)  you would lose $80 if one of your workers missed an entire 8 hour shift. 
A)  the next worker that offers to work an extra 8 hours should receive at least $80. 
B)  you can send someone home 6 hours early and still pay them the $60 they would have earned while on the clock. 
C)  you would be willing pay up to $60 for someone to work another 6 hours. 
D)  you would lose $80 if one of your workers missed an entire 8 hour shift.

Question 10

The ________ represents all permissible combinations of the decision variables in a linear programming model.

Accepted Answer

The answer of The ________ represents all permissible combinations of...

Question 11

Suppose that the optimal values of the decision variables to a two-variable linear programming problem remain the same as long as the slope of the objective function lies between the slopes of the following two constraints:
2X1 + 3X2 ≤ 26
2X1 + 2X2 ≤20
The current objective function is:
8X1+ 9X2 = Z
Which of the following statements about the range of optimality on c1 is TRUE?

Accepted Answer

A)  0 ≤ c1 ≤ 2 
B)  2 ≤ c1 ≤ 6 
C)  6 ≤ c1 ≤ 9 
D)  9 ≤c1 ≤ 12 
A)  0 ≤ c1 ≤ 2 
B)  2 ≤ c1 ≤ 6 
C)  6 ≤ c1 ≤ 9 
D)  9 ≤c1 ≤ 12

Question 12

________ are the limitations that restrict the permissible choices for the decision variables.

Accepted Answer

The answer of ________ are the limitations that restrict the...

Question 13

The CZ Jewelry Company produces two products: (1)engagement rings and (2)jeweled watches.The production process for each is similar in that both require a certain number of hours of diamond work and a certain number of labor hours in the gold department.Each ring takes four hours of diamond work and two hours in the gold shop.Each watch requires three hours in diamonds and one hour in the gold department.There are 240 hours of diamond labor available and 100 hours of gold department time available for the next month.Each engagement ring sold yields a profit of $9; each watch produced may be sold for a $10 profit.
a.Give a complete formulation of this problem,including a careful definition of your decision variables.Let the first decision variable,(X1),deal with rings,the second decision variable,(X2),with watches,the first constraint with diamonds,and the second constraint with gold.
b.Graph the problem fully in the following space.Label the axes carefully,plot the constraints,shade the feasibility region,plot at least one isoprofit line that reveals the optimal solution,circle the corner points and highlight the optimal corner point so found,and solve for it algebraically.(Show all your work to get credit.)

Accepted Answer

a. X₂ Max: 9X₁+ 10X₂ s.t.4X₁ +

Question 14

The Really Big Shoe Company is a manufacturer of basketball shoes and football shoes.Ed Sullivan,the manager of marketing,must decide the best way to spend advertising resources.Each football team sponsored requires 120 pairs of shoes.Each basketball team requires 32 pairs of shoes.Football coaches receive $300,000 for shoe sponsorship and basketball coaches receive $1,000,000.Ed's promotional budget is $30,000,000.The Really Big Shoe Company has a very limited supply (4 liters or 4,000cc)of flubber,a rare and costly raw material used only in promotional athletic shoes.Each pair of basketball shoes requires 3cc of flubber,and each pair of football shoes requires 1cc of flubber.Ed desires to sponsor as many basketball and football teams as resources allow.However,he has already committed to sponsoring 19 football teams and wants to keep his promises.
a.Give a linear programming formulation for Ed.Make the variable definitions and constraints line up with the computer output appended to this exam.
b.Solve the problem graphically,showing constraints,feasible region,and isoprofit lines.Circle the optimal solution,making sure that the isoprofit lines drawn make clear why you chose this point.(Show all your calculations for plotting the constraints and isoprofit line on the left to get credit.)
   
c.Solve algebraically for the corner point on the feasible region.
d.Part of Ed's computer output is shown following.Give a full explanation of the meaning of the three numbers listed at the end.Based on your graphical and algebraic analysis,explain why these numbers make sense.(Hint: He formulated the budget constraint in terms of $000.)
See the computer printout that follows.
Solver-Linear Programming
Solution
 $\begin{array} { r r r r } \text { Variable } & \begin{array} { r } \text { Variable } \ \text { Label } \end{array} & \begin{array} { r } \text { Original } \ \text { Value } \end{array} & \begin{array} { r } \text { Coefficient } \ \text { Sensitivity } \end{array} \ \text { Var1 } & 19.000 C & 1.000 C & 0 \ \text { Var2 } & 17.9167 & 1.000 C & 0 \ \text { Constraint } & \text { Original } & \text { Slack or } & \text { Shadow } \ \text { Label } & \text { RHV } & \text { Surplus } & \text { Price } \ \text { Const1 } & & & \ \text { Const2 } & 19 & 0 & 0 \ \text { Const3 } & 3000 \mathrm { C } & 6383 & 0.0104 \ & 400 \mathrm { C } & 0 & 0 \end{array}$
Objective Function
 Value:                                                                $36.91666667$ 
Sensitivity Analysis and Ranges
Objective Function Coefficients
 $$\begin{array}{l}
\begin{array} { r r r r } 
\begin{array} { r } 
\text { Variable } \
\text { Label }
\end{array} & \begin{array} { r r r } 
\text { Lower } & \text { Original } & \text { Upper } \
\text { Limit }
\end{array} & \text { Coefficient } & \text { Limit } \
\text { Var1 } & \text { No Limit } & 1 & 1.25 \
\text { Var2 } & 0.8 & 1 & \text { No Limit }
\end{array}\
\text { Right-Hand-Side Values }\
\begin{array} { r r r r } 
\text { Constraint } & \begin{array} { r } 
\text { Lower } \
\text { Label }
\end{array} & \begin{array} { r } 
\text { Original } \
\text { Value }
\end{array} & \begin{array} { r } 
\text { Upper } \
\text { Limit }
\end{array} \
\text { Const1 } & 12.2807 & 19 & 33.33333333 \
\text { Const2 } & 23616.67 & 3000 \mathrm { C } & \text { No Limit } \
\text { Const3 } & 228 \mathrm { C } & 400 \mathrm { C } & 4612.8
\end{array}
\end{array}$$ 
First Number: The shadow price of 0.0104 for the "Const3" constraint.
Second Number: The slack or surplus of 6383 for the "Const1" constraint.
Third Number: The lower limit of 12.2807 for the "Const1" constraint.

Accepted Answer

a.LetX₁= the number of football teams spo

Question 15

Which of the following statements regarding linear programming is NOT true?

Accepted Answer

A)  A parameter is also known as a decision variable. 
B)  Linearity assumes proportionality and additivity. 
C)  The product-mix problem is a one-period type of aggregate planning problem. 
D)  One reasonable sequence for formulating a model is defining the decision variables, writing out the objective function, and writing out the constraints. 
A)  A parameter is also known as a decision variable. 
B)  Linearity assumes proportionality and additivity. 
C)  The product-mix problem is a one-period type of aggregate planning problem. 
D)  One reasonable sequence for formulating a model is defining the decision variables, writing out the objective function, and writing out the constraints.

Question 16

In linear programming,each parameter is assumed to be known with certainty.

Accepted Answer

A) True 
 B)False

Question 17

Linear programming is useful for allocating scarce resources among competing demands.

Accepted Answer

A) True 
 B)False

Question 18

You are faced with a linear programming objective function of:
Max P = $20X + $30Y
And constraints of:
3X + 4Y = 24 (Constraint A)
5X -Y = 18 (Constraint B)
You discover that the shadow price for Constraint A is 7.5 and the shadow price for Constraint B is 0.Which of these statements is TRUE?

Accepted Answer

A)  You can change quantities of X and Y at no cost for Constraint B. 
B)  For every additional unit of the objective function you create, you lose 0 units of B. 
C)  For every additional unit of the objective function you create, the price of A rises by $7.50. 
D)  The most you would want to pay for an additional unit of A would be $7.50. 
A)  You can change quantities of X and Y at no cost for Constraint B. 
B)  For every additional unit of the objective function you create, you lose 0 units of B. 
C)  For every additional unit of the objective function you create, the price of A rises by $7.50. 
D)  The most you would want to pay for an additional unit of A would be $7.50.

Question 19

The objective function Maximize Z = 3x² = 4y is appropriate.

Accepted Answer

A) True 
 B)False

Question 20

In linear programming,a ________ is a point that lies at the intersection of two (or possibly more)constraint lines on the boundary of the feasible region.

Accepted Answer

The answer of In linear programming,a ________ is a point...

For the line that has the equation 4X₁ + 8X₂= 88,an axis intercept is

A modeler is limited to two or fewer decision variables when using the ________.

The graphical method is a practical method for solving product mix problems of any size,provided the decision maker has sufficient quantities of graph paper.

A parameter is a region that represents all permissible combinations of the decision variables in a linear programming model.

What are the assumptions of linear programming? Provide examples of each.

Only corner points should be considered for the optimal solution to a linear programming problem.

The ________ is an expression in linear programming models that states mathematically what is being maximized or minimized.

While glancing over the sensitivity report,you note that the stitching labor has a shadow price of $10 and a lower limit of 24 hours with an upper limit of 36 hours.If your original right hand value for stitching labor was 30 hours,you know that

The ________ represents all permissible combinations of the decision variables in a linear programming model.

________ are the limitations that restrict the permissible choices for the decision variables.

Which of the following statements regarding linear programming is NOT true?

In linear programming,each parameter is assumed to be known with certainty.

Linear programming is useful for allocating scarce resources among competing demands.

You are faced with a linear programming objective function of: Max P = $20X + $30Y And constraints of: 3X + 4Y = 24 (Constraint A) 5X -Y = 18 (Constraint B) You discover that the shadow price for Constraint A is 7.5 and the shadow price for Constraint B is 0.Which of these statements is TRUE?

The objective function Maximize Z = 3x² = 4y is appropriate.

In linear programming,a ________ is a point that lies at the intersection of two (or possibly more)constraint lines on the boundary of the feasible region.

Creating Customer Value through Operations

Supply Chain Management

Process Configuration

Capacity

Inventory Management

Quality and Process Improvement

Lean Systems

Managing Projects

Location and Layout

Managing Demand and Forecasting

Operations Planning and Scheduling

Resource Planning

Decision Making

Financial Analysis

Work Measurement

Learning Curve Analysis

Computer-Integrated Manufacturing

Acceptance Sampling Plans

Simulation

Special Inventory Models

Waiting Lines

Filters

Exam 21: Linear Programming

For the line that has the equation 4X1 + 8X2 = 88,an axis intercept is

A modeler is limited to two or fewer decision variables when using the ________.

The graphical method is a practical method for solving product mix problems of any size,provided the decision maker has sufficient quantities of graph paper.

A parameter is a region that represents all permissible combinations of the decision variables in a linear programming model.

What are the assumptions of linear programming? Provide examples of each.

Only corner points should be considered for the optimal solution to a linear programming problem.

The ________ is an expression in linear programming models that states mathematically what is being maximized or minimized.

While glancing over the sensitivity report,you note that the stitching labor has a shadow price of $10 and a lower limit of 24 hours with an upper limit of 36 hours.If your original right hand value for stitching labor was 30 hours,you know that

The ________ represents all permissible combinations of the decision variables in a linear programming model.

________ are the limitations that restrict the permissible choices for the decision variables.

Which of the following statements regarding linear programming is NOT true?

In linear programming,each parameter is assumed to be known with certainty.

Linear programming is useful for allocating scarce resources among competing demands.

You are faced with a linear programming objective function of: Max P = $20X + $30Y And constraints of: 3X + 4Y = 24 (Constraint A) 5X -Y = 18 (Constraint B) You discover that the shadow price for Constraint A is 7.5 and the shadow price for Constraint B is 0.Which of these statements is TRUE?

The objective function Maximize Z = 3x² = 4y is appropriate.

In linear programming,a ________ is a point that lies at the intersection of two (or possibly more)constraint lines on the boundary of the feasible region.

Creating Customer Value through Operations

Supply Chain Management

Process Configuration

Capacity

Inventory Management

Quality and Process Improvement

Lean Systems

Managing Projects

Location and Layout

Managing Demand and Forecasting

Operations Planning and Scheduling

Resource Planning

Decision Making

Financial Analysis

Work Measurement

Learning Curve Analysis

Computer-Integrated Manufacturing

Acceptance Sampling Plans

Simulation

Special Inventory Models

Waiting Lines

Filters

For the line that has the equation 4X₁ + 8X₂= 88,an axis intercept is