Question 1

Solve the following graphically:
Max z = 3x1 + 4x2
s.t. &emsp; x1 + 2x2 ?16
&emsp; &emsp;2x1 + 3x2 ? 18
&emsp; &emsp;x1  ?  2
&emsp; &emsp;x2 ? 10
&emsp; &emsp;x1, x2 ? 0
What are the optimal values of x1, x2, and z?

Accepted Answer

The answer of Solve the following graphically:
Max z = 3x1...

Question 2

Consider the following linear program:
MIN Z = 60A + 50B
s.t.&emsp; 10A + 20B ? 200
&emsp; &emsp;8A + 5B ? 80
&emsp; &emsp;A ? 2
&emsp; &emsp;B ? 5
Solve this linear program graphically and determine the optimal quantities of A, B, and the value of Z.

Accepted Answer

The answer of Consider the following linear program:
MIN Z =...

Question 3

The constraint 2X +XY violates the ________ property of linear programming.

Accepted Answer

The answer of The constraint 2X +XY violates the ________...

Question 4

If the objective function is parallel to a constraint, the linear program could have ________.

Accepted Answer

The answer of If the objective function is parallel to...

Question 5

The management scientist constructed a linear program to help the alchemist maximize his gold production process. The computer model chugged away for a few minutes and returned an answer of infinite profit., which is what might be expected from a(n) ________ problem.

Accepted Answer

The answer of The management scientist constructed a linear program...

Question 6

In a constraint, the ________ variable represents unused resources.

Accepted Answer

The answer of In a constraint, the ________ variable represents...

Question 7

________ are at the endpoints of the constraint line segment that the objective function parallels.

Accepted Answer

The answer of ________ are at the endpoints of the...

Question 8

Consider the following minimization problem:
Min z = x1 + 2x2
&emsp; &emsp;s.t. x1 + x2 ? 300
&emsp; &emsp;2x1 + x2 ? 400
&emsp; &emsp;2x1 + 5x2 ? 750
&emsp; &emsp;x1, x2 ? 0
Which constraints are binding at the optimal solution? (x1 =250, x2 = 50)

Accepted Answer

The answer of Consider the following minimization problem:
Min z =...

Question 9

A graphical representation of a linear program is shown below. The shaded area represents the feasible region, and the dashed line in the middle is the slope of the objective function.  
If this is a maximization, which extreme point is the optimal solution?

Accepted Answer

The answer of A graphical representation of a linear program...

Question 10

________ is the difference between the left- and right-hand sides of a greater than or equal to constraint.

Accepted Answer

The answer of ________ is the difference between the left-...

Question 11

The best feasible solution is ________.

Accepted Answer

The answer of The best feasible solution is ________....

Question 12

Corner points on the boundary of the feasible solution area are called ________ points.

Accepted Answer

The answer of Corner points on the boundary of the...

Question 13

A linear programming problem that results in a solution that is ________ usually indicates that the linear program has been incorrectly formulated.

Accepted Answer

The answer of A linear programming problem that results in...

Question 14

Consider the following linear program:
MAX Z = 60A + 50B
s.t.&emsp; 10A + 20B ? 200
&emsp; &emsp;8A + 5B ? 80
&emsp; &emsp;A ? 2
&emsp; &emsp;B ? 5
Solve this linear program graphically and determine the optimal quantities of A, B, and the value of Z.

Accepted Answer

The answer of Consider the following linear program:
MAX Z =...

Question 15

Consider the following minimization problem:
Min z = x1 + 2x2
s.t. &ensp;     x1 + x2 ? 300
&emsp; &emsp; 2x1 + x2 ? 400
&emsp; &emsp; 2x1 + 5x2 ? 750
&emsp; &emsp; x1, x2 ? 0
What is the optimal solution?

Accepted Answer

The answer of Consider the following minimization problem:
Min z =...

Question 16

The ________ property of linear programming models indicates that the values of all the model parameters are known and are assumed to be constant.

Accepted Answer

The answer of The ________ property of linear programming models...

Question 17

The ________ step in formulating a linear programming model is to define the decision variables.

Accepted Answer

The answer of The ________ step in formulating a linear...

Question 18

The ________ property of linear programming models indicates that the rate of change, or slope, of the objective function or a constraint is constant.

Accepted Answer

The answer of The ________ property of linear programming models...

Question 19

The ________ property of linear programming models indicates that the decision variables cannot be restricted to integer values and can take on any fractional value.

Accepted Answer

The answer of The ________ property of linear programming models...

Question 20

A graphical representation of a linear program is shown below. The shaded area represents the feasible region, and the dashed line in the middle is the slope of the objective function.  
If this is a minimization, which extreme point is the optimal solution?

Accepted Answer

The answer of A graphical representation of a linear program...

Quiz 2: Linear Programming: Model Formulation and Graphical Solution

Solve the following graphically: Max z = 3x1 + 4x2 s.t. x1 + 2x2 ?16 2x1 + 3x2 ? 18 x1 ? 2 x2 ? 10 x1, x2 ? 0 What are the optimal values of x1, x2, and z?

Consider the following linear program: MIN Z = 60A + 50B s.t. 10A + 20B ? 200 8A + 5B ? 80 A ? 2 B ? 5 Solve this linear program graphically and determine the optimal quantities of A, B, and the value of Z.

The constraint 2X +XY violates the ________ property of linear programming.

If the objective function is parallel to a constraint, the linear program could have ________.

The management scientist constructed a linear program to help the alchemist maximize his gold production process. The computer model chugged away for a few minutes and returned an answer of infinite profit., which is what might be expected from a(n) ________ problem.

In a constraint, the ________ variable represents unused resources.

________ are at the endpoints of the constraint line segment that the objective function parallels.

Consider the following minimization problem: Min z = x1 + 2x2 s.t. x1 + x2 ? 300 2x1 + x2 ? 400 2x1 + 5x2 ? 750 x1, x2 ? 0 Which constraints are binding at the optimal solution? (x1 =250, x2 = 50)

A graphical representation of a linear program is shown below. The shaded area represents the feasible region, and the dashed line in the middle is the slope of the objective function. If this is a maximization, which extreme point is the optimal solution?

________ is the difference between the left- and right-hand sides of a greater than or equal to constraint.

The best feasible solution is ________.

Corner points on the boundary of the feasible solution area are called ________ points.

A linear programming problem that results in a solution that is ________ usually indicates that the linear program has been incorrectly formulated.

Consider the following linear program: MAX Z = 60A + 50B s.t. 10A + 20B ? 200 8A + 5B ? 80 A ? 2 B ? 5 Solve this linear program graphically and determine the optimal quantities of A, B, and the value of Z.

Consider the following minimization problem: Min z = x1 + 2x2 s.t. x1 + x2 ? 300 2x1 + x2 ? 400 2x1 + 5x2 ? 750 x1, x2 ? 0 What is the optimal solution?

The ________ property of linear programming models indicates that the values of all the model parameters are known and are assumed to be constant.

The ________ step in formulating a linear programming model is to define the decision variables.

The ________ property of linear programming models indicates that the rate of change, or slope, of the objective function or a constraint is constant.

The ________ property of linear programming models indicates that the decision variables cannot be restricted to integer values and can take on any fractional value.

A graphical representation of a linear program is shown below. The shaded area represents the feasible region, and the dashed line in the middle is the slope of the objective function. If this is a minimization, which extreme point is the optimal solution?