Question 1

Consider the following linear programming problem: Maximize 20X + 30Y
Subject to: X + Y ≤ 80
12X + 12Y ≤ 600
3X + 2Y ≤ 400
X, Y ≥ 0
This is a special case of a linear programming problem in which

Accepted Answer

The constraint 12X + 12Y ≤ 600 can be simplified to X + Y ≤ 50, which is stricter than the constraint X + Y ≤ 80, making the latter redundant. The problem can still be solved graphically, and there's no indication of no feasible solution or multiple optimal solutions without further analysis.

Question 2

In order for a linear programming problem to have multiple solutions, the solution must exist

Accepted Answer

For a linear programming problem to have multiple solutions, the solution set must lie along a constraint line that is parallel to the objective function. This means that as you move along this constraint line, the value of the objective function remains constant, indicating multiple optimal solutions.

Question 3

The optimal solution to this linear program is

Accepted Answer

The answer of The optimal solution to this linear program...

Question 4

Consider the following linear programming problem: Maximize 5X + 6Y
Subject to: 4X + 2Y ≤ 420
1X + 2Y ≤ 120
All variables ≥ 0
Which of the following points (X,Y)is in the feasible region?

Accepted Answer

The answer of Consider the following linear programming problem: Maximize...

Question 5

A straight line representing all non-negative combinations of X₁ and X₂ for a particular profit level is called a(n)

Accepted Answer

An isoprofit line represents all non-negative combinations of two decision variables (in this case, X₁ and X₂) that result in a particular level of profit. Therefore, the correct choice is D: isoprofit line.

Question 6

Which of the following constraints are binding?

Accepted Answer

The constraint "Extrusion only" is not binding as there are other options for manufacturing. The constraint "Packing only" is also not binding as there are other ways to package the product. The constraint "Additive only" is not mentioned as a constraint in the context given. Therefore, "Extrusion and Packaging" is the only constraint that is binding as it limits the type of manufacturing and packaging methods that can be used.

Question 7

Consider the following linear programming problem: Maximize 5X + 6Y
Subject to: 4X + 2Y ≤ 420
1X + 2Y ≤ 120
All variables ≥ 0
Which of the following points (X,Y)is feasible?

Accepted Answer

To determine feasibility, we need to check if the given points satisfy all the constraints. 
A) (50,40): 
4(50) + 2(40) = 300 ≤ 420 ✔️
1(50) + 2(40) = 130 ≤ 120 ❌
Not feasible as it violates one of the constraints. 
B) (30,50): 
4(30) + 2(50) = 220 ≤ 420 ✔️
1(30) + 2(50) = 130 ≤ 120 ❌
Not feasible as it violates one of the constraints. 
C) (60,30): 
4(60) + 2(30) = 300 ≤ 420 ✔️
1(60) + 2(30) = 120 ≤ 120 ✔️
Feasible as it satisfies all the constraints. 
D) (90,20):
4(90) + 2(20) = 380 ≤ 420 ✔️
1(90) + 2(20) = 130 ≤ 120 ❌
Not feasible as it violates one of the constraints.

Therefore, the only feasible point is (60,30), and it is the best choice as it satisfies all the constraints and maximizes the objective function.

Question 8

What is the increase in the objective value if 2 units of additive are added?

Accepted Answer

The answer of What is the increase in the objective...

Question 9

A constraint with positive slack or surplus is called a

Accepted Answer

A constraint with positive slack or surplus indicates that the constraint is not binding, meaning that the available resources are not fully utilized.

Question 10

Which of the following is not an assumption of LP?

Accepted Answer

Linear Programming (LP) assumes certainty, proportionality, and divisibility in its models, but it does not assume multiplicativity. Multiplicativity would imply that variables can interact in a multiplicative way, which is not a standard assumption in linear programming models. Linear programming models are based on linear relationships.

Question 11

The coefficients of the variables in the constraint equations that represent the amount of resources needed to produce one unit of the variable are called

Accepted Answer

Technological coefficients represent the resources needed to produce one unit of the variable, and are commonly used in linear programming. Objective coefficients are the coefficients of the variables in the objective function, while shadow prices and dual prices represent the values of the slack variables in the optimal solution.

Question 12

Consider the following constraints from a linear programming problem: 2X + Y ≤ 200
X + 2Y ≤ 200
X, Y ≥ 0
If these are the only constraints, which of the following points (X,Y)cannot be the optimal solution?

Accepted Answer

Substituting (0,200) into the constraints, we get:
2(0) + 200 ≤ 200, which is true
(0) + 2(200) ≤ 200, which is false
Since one of the constraints is not satisfied by (0,200), it cannot be the optimal solution.

Question 13

What is the increase in the objective value if 2 units of packaging are added?

Accepted Answer

The increase in the objective value is determined by the shadow price or dual value associated with the constraint for packaging. If the shadow price is 11 per unit, adding 2 units would increase the objective value by 2 * 11 = 22.

Question 14

Consider the following linear programming problem: Maximize 12X + 10Y
Subject to: 4X + 3Y ≤ 480
2X + 3Y ≤ 360
All variables ≥ 0
Which of the following points (X,Y)is feasible?

Accepted Answer

The point (30,100) satisfies both constraints: 4(30) + 3(100) = 420 ≤ 480 and 2(30) + 3(100) = 360 ≤ 360.

Question 15

Consider the following linear programming problem: Maximize 10X + 30Y
Subject to: X + 2Y ≤ 80
8X + 16Y ≤ 640
4X + 2Y ≥ 100
X, Y ≥ 0
This is a special case of a linear programming problem in which

Accepted Answer

Constraint 4X + 2Y ≥ 100 is a redundant constraint as it is already implied by constraint X + 2Y ≤ 80. Therefore, it can be omitted from the problem without affecting the feasible region or the optimal solution.

Question 16

Which of the following functions is not linear?

Accepted Answer

A function is linear if it has a constant rate of change, meaning that the change in the output value is proportional to the change in the input value. In function C, the term 5YZ makes it non-linear because the rate of change of Y is dependent on Z as well, which violates the condition of constant rate of change. The other options have a constant rate of change and are linear functions. Additionally, option D is a constant function, which is also considered linear.

Question 17

In order for a linear programming problem to have a unique solution, the solution must exist

Accepted Answer

In order for a linear programming problem to have a unique solution, the solution must exist at the intersection of two or more constraints. This is because the objective function can be optimized at multiple points, but only the intersection of multiple constraints will limit the feasible region to a single point.

Question 18

What is the increase in the objective value if 2 units of extrusion are added?

Accepted Answer

The increase in the objective value is determined by the shadow price or dual value associated with the constraint for extrusion. If the shadow price is 3 per unit, then adding 2 units results in an increase of 6.

Question 19

Which of the following is not one of the steps in formulating a linear program?

Accepted Answer

Graphing the constraints to determine the feasible region is a step in solving a linear program, not in formulating it. Formulating a linear program involves defining decision variables, writing mathematical expressions for the objective function and constraints, and identifying the objective and constraints.

Question 20

What type of problems use LP to decide how much of each product to make, given a series of resource restrictions?

Accepted Answer

Linear Programming (LP) is commonly used to solve product mix problems, where the objective is to determine the optimal quantity of each product to produce, given a set of constraints such as resource limitations, to maximize profit or minimize costs.

Quiz 7: Linear Programming Models: Graphical and Computer Methods

Consider the following linear programming problem: Maximize 20X + 30Y Subject to: X + Y ≤ 80 12X + 12Y ≤ 600 3X + 2Y ≤ 400 X, Y ≥ 0 This is a special case of a linear programming problem in which

In order for a linear programming problem to have multiple solutions, the solution must exist

The optimal solution to this linear program is

Consider the following linear programming problem: Maximize 5X + 6Y Subject to: 4X + 2Y ≤ 420 1X + 2Y ≤ 120 All variables ≥ 0 Which of the following points (X,Y) is in the feasible region?

A straight line representing all non-negative combinations of X₁ and X₂ for a particular profit level is called a(n)

Which of the following constraints are binding?

Consider the following linear programming problem: Maximize 5X + 6Y Subject to: 4X + 2Y ≤ 420 1X + 2Y ≤ 120 All variables ≥ 0 Which of the following points (X,Y) is feasible?

What is the increase in the objective value if 2 units of additive are added?

A constraint with positive slack or surplus is called a

Which of the following is not an assumption of LP?

The coefficients of the variables in the constraint equations that represent the amount of resources needed to produce one unit of the variable are called

Consider the following constraints from a linear programming problem: 2X + Y ≤ 200 X + 2Y ≤ 200 X, Y ≥ 0 If these are the only constraints, which of the following points (X,Y) cannot be the optimal solution?

What is the increase in the objective value if 2 units of packaging are added?

Consider the following linear programming problem: Maximize 12X + 10Y Subject to: 4X + 3Y ≤ 480 2X + 3Y ≤ 360 All variables ≥ 0 Which of the following points (X,Y) is feasible?

Consider the following linear programming problem: Maximize 10X + 30Y Subject to: X + 2Y ≤ 80 8X + 16Y ≤ 640 4X + 2Y ≥ 100 X, Y ≥ 0 This is a special case of a linear programming problem in which

Which of the following functions is not linear?

In order for a linear programming problem to have a unique solution, the solution must exist

What is the increase in the objective value if 2 units of extrusion are added?

Which of the following is not one of the steps in formulating a linear program?

What type of problems use LP to decide how much of each product to make, given a series of resource restrictions?

Quiz 7: Linear Programming Models: Graphical and Computer Methods

Consider the following linear programming problem: Maximize 20X + 30Y Subject to: X + Y ≤ 80 12X + 12Y ≤ 600 3X + 2Y ≤ 400 X, Y ≥ 0 This is a special case of a linear programming problem in which

In order for a linear programming problem to have multiple solutions, the solution must exist

The optimal solution to this linear program is

Consider the following linear programming problem: Maximize 5X + 6Y Subject to: 4X + 2Y ≤ 420 1X + 2Y ≤ 120 All variables ≥ 0 Which of the following points (X,Y) is in the feasible region?

A straight line representing all non-negative combinations of X1 and X2 for a particular profit level is called a(n)

Which of the following constraints are binding?

Consider the following linear programming problem: Maximize 5X + 6Y Subject to: 4X + 2Y ≤ 420 1X + 2Y ≤ 120 All variables ≥ 0 Which of the following points (X,Y) is feasible?

What is the increase in the objective value if 2 units of additive are added?

A constraint with positive slack or surplus is called a

Which of the following is not an assumption of LP?

The coefficients of the variables in the constraint equations that represent the amount of resources needed to produce one unit of the variable are called

Consider the following constraints from a linear programming problem: 2X + Y ≤ 200 X + 2Y ≤ 200 X, Y ≥ 0 If these are the only constraints, which of the following points (X,Y) cannot be the optimal solution?

What is the increase in the objective value if 2 units of packaging are added?

Consider the following linear programming problem: Maximize 12X + 10Y Subject to: 4X + 3Y ≤ 480 2X + 3Y ≤ 360 All variables ≥ 0 Which of the following points (X,Y) is feasible?

Consider the following linear programming problem: Maximize 10X + 30Y Subject to: X + 2Y ≤ 80 8X + 16Y ≤ 640 4X + 2Y ≥ 100 X, Y ≥ 0 This is a special case of a linear programming problem in which

Which of the following functions is not linear?

In order for a linear programming problem to have a unique solution, the solution must exist

What is the increase in the objective value if 2 units of extrusion are added?

Which of the following is not one of the steps in formulating a linear program?

What type of problems use LP to decide how much of each product to make, given a series of resource restrictions?

A straight line representing all non-negative combinations of X₁ and X₂ for a particular profit level is called a(n)