Question 1

The region that satisfies all of the constraints in linear programming is called the region of optimality.

Accepted Answer

A) True 
 B)False  False

Question 2

Explain how to use the iso-profit line in a graphical solution to maximization problem.

Accepted Answer

The iso-profit line is moved up in a maximization problem until it no longer intersects with any constraint equation.The last point in the feasible region that the line touches is the optimal solution.

Question 3

What are corner points? What is their relevance to solving linear programming problems?

Accepted Answer

Corner points are the intersections of the constraints that form the feasible region.While all points in the feasible region are possible,an optimal solution will always be at a corner point.Therefore,one method of solving linear programming problems involves the identification and valuation of all corner points.

Question 4

________ are restrictions that limit the degree to which a manager can pursue an objective.

Accepted Answer

The answer of ________ are restrictions that limit the degree...

Question 5

If we wish to ensure that decision variable values in a linear program are integers rather than fractions,the generally accepted practice is to round the solutions to the nearest integer values.

Accepted Answer

A) True 
 B)False

Question 6

Constraints are needed to solve linear programming problems by hand,but not by computer.

Accepted Answer

A) True 
 B)False

Question 7

What is the feasible region in a linear programming problem?

Accepted Answer

The feasible region

Question 8

What is linear programming?

Accepted Answer

Linear programming is a mathem

Question 9

In linear programming,statements such as "the blend must consist of at least 10% of ingredient A,at least 30% of ingredient B,and no more than 50% of ingredient C" can be made into valid constraints even though the percentages do not add up to 100 percent.

Accepted Answer

A) True 
 B)False

Question 10

The main disadvantage of introducing constraints into a linear program that enforce some or all of the decision variables to be either integer or binary is that:

Accepted Answer

A) the programs may take longer to solve. 
B) the solutions will no longer be optimal. 
C) Excel can no longer be used to solve the program. 
D) the constraints are difficult to formulate. 
E) we cannot have "yes-or-no" decisions in the linear program. 
A) the programs may take longer to solve. 
B) the solutions will no longer be optimal. 
C) Excel can no longer be used to solve the program. 
D) the constraints are difficult to formulate. 
E) we cannot have "yes-or-no" decisions in the linear program.

Question 11

Identify three examples of resources that are typically constrained in a linear programming problem.

Accepted Answer

The textbook gives m

Question 12

The corner-point solution method requires:

Accepted Answer

A) identifying the corner of the feasible region that has the sharpest angle. 
B) moving the iso-profit line to the highest level that still touches some part of the feasible region. 
C) moving the iso-profit line to the lowest level that still touches some part of the feasible region. 
D) finding the coordinates at each corner of the feasible solution space. 
E) none of the above 
A) identifying the corner of the feasible region that has the sharpest angle. 
B) moving the iso-profit line to the highest level that still touches some part of the feasible region. 
C) moving the iso-profit line to the lowest level that still touches some part of the feasible region. 
D) finding the coordinates at each corner of the feasible solution space. 
E) none of the above

Question 13

Computer software provides a simple way to guarantee only integer solutions to linear programming problems.

Accepted Answer

A) True 
 B)False

Question 14

A linear programming problem has two constraints 2X + 4Y ≤ 100 and 1X + 8Y ≤ 100,plus nonnegativity constraints on X and Y.Which of the following statements about its feasible region is TRUE?

Accepted Answer

A) There are four corner points including (50,0)and (0,12.5). 
B) The two corner points are (0,0)and (50,12.5). 
C) The graphical origin (0,0)is not in the feasible region. 
D) The feasible region includes all points that satisfy one constraint,the other,or both. 
E) The feasible region cannot be determined without knowing whether the problem is to be minimized or maximized. 
A) There are four corner points including (50,0)and (0,12.5). 
B) The two corner points are (0,0)and (50,12.5). 
C) The graphical origin (0,0)is not in the feasible region. 
D) The feasible region includes all points that satisfy one constraint,the other,or both. 
E) The feasible region cannot be determined without knowing whether the problem is to be minimized or maximized.

Question 15

Riker Co.is considering which of 4 different projects to undertake in order to maximize its net present value (NPV).Define Xi as a binary variable that equals 1 if project i is undertaken and 0 otherwise,for i = 1,2,3,4.The NPV and required capital (in millions)for each project are listed below.
  Which of the following represents the constraint(s)stating that project 1 must be undertaken and at least one of the other projects must be undertaken?

Accepted Answer

A) X1 + X2 ≤ 1,and X1 + X3 ≤ 1,and X1 + X4 ≤ 1 
B) X1 ≥1,and X2 + X3 + X4 ≥ 1 
C) X1 + X2 ≥ 1,and X1 + X3 ≥ 1,and X1 + X4 ≥ 1 
D) X1 ≥1,and X2 + X3 + X4 ≤ 3 
E) X1 + X2 + X3 + X4 ≥ 2 
A) X1 + X2 ≤ 1,and X1 + X3 ≤ 1,and X1 + X4 ≤ 1 
B) X1 ≥1,and X2 + X3 + X4 ≥ 1 
C) X1 + X2 ≥ 1,and X1 + X3 ≥ 1,and X1 + X4 ≥ 1 
D) X1 ≥1,and X2 + X3 + X4 ≤ 3 
E) X1 + X2 + X3 + X4 ≥ 2

Question 16

Riker Co.is considering which of 4 different projects to undertake in order to maximize its net present value (NPV).Define Xi as a binary variable that equals 1 if project i is undertaken and 0 otherwise,for i = 1,2,3,4.The NPV and required capital (in millions)for each project are listed below.
  What is the proper objective function?

Accepted Answer

A) Max X1 + X2 + X3 + X4 
B) Min 60X1 + 50X2 + 40X3 + 20X4 
C) Max 60X1 + 50X2 + 40X3 + 20X4 
D) Max 7X1 + 10X2 + 6X3 + 3X4 
E) Max 170(X1 + X2 + X3 + X4) 
A) Max X1 + X2 + X3 + X4 
B) Min 60X1 + 50X2 + 40X3 + 20X4 
C) Max 60X1 + 50X2 + 40X3 + 20X4 
D) Max 7X1 + 10X2 + 6X3 + 3X4 
E) Max 170(X1 + X2 + X3 + X4)

Question 17

A linear programming problem contains a restriction that reads "the quantity of Q must be at least as large as the sum of R,S,and T." Formulate this as a linear programming constraint.

Accepted Answer

Q ≥ R + S

Question 18

A manager must decide on the mix of products to produce for the coming week.Product A requires three minutes per unit for molding,two minutes per unit for painting,and one minute for packing.Product B requires two minutes per unit for molding,four minutes for painting,and three minutes per unit for packing.There will be 600 minutes available for molding,600 minutes for painting,and 420 minutes for packing.Both products have contributions of $1.50 per unit.Answer the following questions;base your work on the solution panel provided.
   a.What combination of A and B will maximize contribution?
b.What is the maximum possible contribution?
c.Are any resources not fully used up? Explain.

Accepted Answer

Maximum contribution occurs at A = 150,B

Question 19

Capital Co.is considering 5 different projects.Define Xi as a binary variable that equals 1 if project i is undertaken and 0 otherwise,for i = 1,2,3,4,5.Which of the following represents the constraint(s)stating that projects 2,3,and 4 cannot all three be undertaken simultaneously?

Accepted Answer

A) X2 + X3 + X4 ≤ 3 
B) X1 + X2 + X3 + X4 + X5 ≤ 3 
C) X2 + X3 + X4 ≤ 1 
D) X2 + X3 + X4 ≤ 2 
E) X2 + X3 ≤ 1 and X3 + X4 ≤ 1 
A) X2 + X3 + X4 ≤ 3 
B) X1 + X2 + X3 + X4 + X5 ≤ 3 
C) X2 + X3 + X4 ≤ 1 
D) X2 + X3 + X4 ≤ 2 
E) X2 + X3 ≤ 1 and X3 + X4 ≤ 1

Question 20

A feedlot is trying to decide on the lowest cost mix that will still provide adequate nutrition for its cattle.Suppose that the numbers in the chart represent the number of grams of ingredient per 100 grams of feed and that the cost of Feed X is $5/100grams,Feed Y is $3/100 grams,and Feed X is $8/100 grams.Each cow will need 50 grams of A per day,20 grams of B,30 grams of C,and 10 grams of D.The feedlot can get no more than 200 grams per day per cow of any of the feed types.Formulate the problem as a linear program.

Accepted Answer

Let X,Y,Z be number of grams of each res

Exam 23: Linear Programming

The region that satisfies all of the constraints in linear programming is called the region of optimality.

Explain how to use the iso-profit line in a graphical solution to maximization problem.

What are corner points? What is their relevance to solving linear programming problems?

________ are restrictions that limit the degree to which a manager can pursue an objective.

If we wish to ensure that decision variable values in a linear program are integers rather than fractions,the generally accepted practice is to round the solutions to the nearest integer values.

Constraints are needed to solve linear programming problems by hand,but not by computer.

What is the feasible region in a linear programming problem?

What is linear programming?

In linear programming,statements such as "the blend must consist of at least 10% of ingredient A,at least 30% of ingredient B,and no more than 50% of ingredient C" can be made into valid constraints even though the percentages do not add up to 100 percent.

The main disadvantage of introducing constraints into a linear program that enforce some or all of the decision variables to be either integer or binary is that:

Identify three examples of resources that are typically constrained in a linear programming problem.

The corner-point solution method requires:

Computer software provides a simple way to guarantee only integer solutions to linear programming problems.

A linear programming problem has two constraints 2X + 4Y ≤ 100 and 1X + 8Y ≤ 100,plus nonnegativity constraints on X and Y.Which of the following statements about its feasible region is TRUE?

A linear programming problem contains a restriction that reads "the quantity of Q must be at least as large as the sum of R,S,and T." Formulate this as a linear programming constraint.

Capital Co.is considering 5 different projects.Define Xi as a binary variable that equals 1 if project i is undertaken and 0 otherwise,for i = 1,2,3,4,5.Which of the following represents the constraint(s)stating that projects 2,3,and 4 cannot all three be undertaken simultaneously?

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