Question 1

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

Accepted Answer

Corner points are the intersections of t

Question 2

A linear programming problem contains a restriction that reads "the quantity of S must be no less than one-fourth as large as T and U combined." Formulate this as a linear programming constraint.

Accepted Answer

A) S / (T + U)≥ 4 
B) S - .25T -.25U ≥ 0 
C) 4S ≤ T + U 
D) S ≥ 4T / 4U 
E) S ≥ .25T + S ≥ .25U 
A) S / (T + U)≥ 4 
B) S - .25T -.25U ≥ 0 
C) 4S ≤ T + U 
D) S ≥ 4T / 4U 
E) S ≥ .25T + S ≥ .25U

Question 3

Suppose that an iso-profit line is given to be X + Y = 10.Which of the following represents another iso-profit line for the same scenario?

Accepted Answer

A) X + Y = 15 
B) X - Y = 10 
C) Y - X = 10 
D) 2X + Y = 10 
E) none of the above 
A) X + Y = 15 
B) X - Y = 10 
C) Y - X = 10 
D) 2X + Y = 10 
E) none of the above

Question 4

Which of the following is not a requirement of a linear programming problem?

Accepted Answer

A) an objective function,expressed in linear terms 
B) constraints,expressed as linear equations or inequalities 
C) an objective function to be maximized or minimized 
D) alternative courses of action 
E) one constraint or resource limit for each decision variable 
A) an objective function,expressed in linear terms 
B) constraints,expressed as linear equations or inequalities 
C) an objective function to be maximized or minimized 
D) alternative courses of action 
E) one constraint or resource limit for each decision variable

Question 5

Sensitivity analysis can be applied to linear programming solutions by either (1)trial and error or (2)the analytic postoptimality method.

Accepted Answer

A) True 
 B)False

Question 6

________ 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 7

The requirements of linear programming problems include an objective function,the presence of constraints,objective and constraints expressed in linear equalities or inequalities,and ________.

Accepted Answer

alternativ

Question 8

In the graphical solution to a linear program,the region that satisfies the constraint 4X + 15Z ≥ 1000 includes the origin of the graph.

Accepted Answer

A) True 
 B)False

Question 9

A difference between minimization and maximization problems is that:

Accepted Answer

A) minimization problems cannot be solved with the corner-point method. 
B) maximization problems often have unbounded regions. 
C) minimization problems often have unbounded regions. 
D) minimization problems cannot have shadow prices. 
E) minimization problems are more difficult to solve than maximization problems. 
A) minimization problems cannot be solved with the corner-point method. 
B) maximization problems often have unbounded regions. 
C) minimization problems often have unbounded regions. 
D) minimization problems cannot have shadow prices. 
E) minimization problems are more difficult to solve than maximization problems.

Question 10

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 11

For a linear programming problem with the constraints 2X + 4Y ≤ 100 and 1X + 8Y ≤ 100,two of its corner points are (0,0)and (0,25).

Accepted Answer

A) True 
 B)False

Question 12

Consider the following constraints from a two-variable linear program:X ≥ 1;Y ≥ 1;X + Y ≤ 9. If these are the only constraints,which of the following points (X,Y)CANNOT be the optimal solution?

Accepted Answer

A) (1,1) 
B) (1,8) 
C) (8,1) 
D) (4,4) 
E) The question cannot be answered without knowing the objective function. 
A) (1,1) 
B) (1,8) 
C) (8,1) 
D) (4,4) 
E) The question cannot be answered without knowing the objective function.

Question 13

What is sensitivity analysis?

Accepted Answer

Sensitivity analysis projects

Question 14

A common form of the product-mix linear programming problem seeks to find that combination of products and the quantity of each that maximizes profit in the presence of limited resources.

Accepted Answer

A) True 
 B)False

Question 15

A linear programming problem has three constraints,plus nonnegativity constraints on X and Y.The constraints are: 2X + 10Y ≤ 100; 4X + 6Y ≤ 120; 6X + 3Y ≥ 90. What is the largest quantity of X that can be made without violating any of these constraints?

Accepted Answer

A) 50 
B) 30 
C) 20 
D) 15 
E) 10 
A) 50 
B) 30 
C) 20 
D) 15 
E) 10

Question 16

Which of the following represents a valid constraint in linear programming?

Accepted Answer

A) 2X ≥ 7XY 
B) (2X)(7Y)≥ 500 
C) 2X + 7Y ≥100 
D) 2X2 + 7Y ≥ 50 
E) All of the above are valid linear programming constraints. 
A) 2X ≥ 7XY 
B) (2X)(7Y)≥ 500 
C) 2X + 7Y ≥100 
D) 2X2 + 7Y ≥ 50 
E) All of the above are valid linear programming constraints.

Question 17

A firm makes two products,Y and Z.Each unit of Y costs $10 and sells for $40.Each unit of Z costs $5 and sells for $25.If the firm's goal were to maximize profit,what would be the appropriate objective function?

Accepted Answer

A) Maximize profit = $40Y = $25Z 
B) Maximize profit = $40Y + $25Z 
C) Maximize profit = $30Y + $20Z 
D) Maximize profit = 0.25Y + 0.20Z 
E) Maximize profit = $50(Y + Z) 
A) Maximize profit = $40Y = $25Z 
B) Maximize profit = $40Y + $25Z 
C) Maximize profit = $30Y + $20Z 
D) Maximize profit = 0.25Y + 0.20Z 
E) Maximize profit = $50(Y + Z)

Question 18

The feasible region in the diagram below is consistent with which one of the following constraints?

Accepted Answer

A) 8X1 + 4X2 ≥ 160 
B) 4X1 + 8X2 ≤ 160 
C) 8X1 - 4X2 ≤ 160 
D) 8X1 + 4X2 ≤ 160 
E) 4X1 - 8X2 ≤ 160 
A) 8X1 + 4X2 ≥ 160 
B) 4X1 + 8X2 ≤ 160 
C) 8X1 - 4X2 ≤ 160 
D) 8X1 + 4X2 ≤ 160 
E) 4X1 - 8X2 ≤ 160

Question 19

What combination of x and y will yield the optimum for this problem? 
Maximize $3x + $15y,subject to 
(1)2x + 4y ≤ 12 and 
(2)5x + 2y ≤ 10 and 
(3)x,y ≥ 0.

Accepted Answer

A) x = 2,y = 0 
B) x = 0,y = 3 
C) x = 0,y = 0 
D) x = 1,y = 5 
E) x = 0,y = 5 
A) x = 2,y = 0 
B) x = 0,y = 3 
C) x = 0,y = 0 
D) x = 1,y = 5 
E) x = 0,y = 5

Question 20

A linear programming problem contains a restriction that reads "the quantity of X must be at least twice as large as the quantity of Y." Formulate this as a linear programming constraint.

Accepted Answer

X ≥ 2Y; al

Exam 23: Linear Programming

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

A linear programming problem contains a restriction that reads "the quantity of S must be no less than one-fourth as large as T and U combined." Formulate this as a linear programming constraint.

Suppose that an iso-profit line is given to be X + Y = 10.Which of the following represents another iso-profit line for the same scenario?

Which of the following is not a requirement of a linear programming problem?

Sensitivity analysis can be applied to linear programming solutions by either (1)trial and error or (2)the analytic postoptimality method.

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

The requirements of linear programming problems include an objective function,the presence of constraints,objective and constraints expressed in linear equalities or inequalities,and ________.

In the graphical solution to a linear program,the region that satisfies the constraint 4X + 15Z ≥ 1000 includes the origin of the graph.

A difference between minimization and maximization problems is that:

For a linear programming problem with the constraints 2X + 4Y ≤ 100 and 1X + 8Y ≤ 100,two of its corner points are (0,0)and (0,25).

Consider the following constraints from a two-variable linear program:X ≥ 1;Y ≥ 1;X + Y ≤ 9. If these are the only constraints,which of the following points (X,Y)CANNOT be the optimal solution?

What is sensitivity analysis?

A common form of the product-mix linear programming problem seeks to find that combination of products and the quantity of each that maximizes profit in the presence of limited resources.

A linear programming problem has three constraints,plus nonnegativity constraints on X and Y.The constraints are: 2X + 10Y ≤ 100; 4X + 6Y ≤ 120; 6X + 3Y ≥ 90. What is the largest quantity of X that can be made without violating any of these constraints?

Which of the following represents a valid constraint in linear programming?

A firm makes two products,Y and Z.Each unit of Y costs $10 and sells for $40.Each unit of Z costs $5 and sells for $25.If the firm's goal were to maximize profit,what would be the appropriate objective function?

The feasible region in the diagram below is consistent with which one of the following constraints?

What combination of x and y will yield the optimum for this problem? Maximize $3x + $15y,subject to (1)2x + 4y ≤ 12 and (2)5x + 2y ≤ 10 and (3)x,y ≥ 0.

A linear programming problem contains a restriction that reads "the quantity of X must be at least twice as large as the quantity of Y." Formulate this as a linear programming constraint.

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