Q: When graphing the solution set for a strict linear inequality such as $3x - 4y < 12$, how should the boundary line be drawn?

As a dashed line to indicate points on the line are not included.

Q: A solution set to a system of linear inequalities is said to be bounded if:

The region can be completely enclosed by a circle.

Q: In the context of linear programming, what does a non-negativity constraint ensure?

Variables must be greater than or equal to zero.

Q: If the feasible region for a linear programming problem is unbounded, which of the following statements is true?

The region cannot be completely enclosed by a circle.

Q: Which of the following systems of inequalities would produce a feasible region that is a triangle in the first quadrant?

$x \geq 0$, $y \geq 0$, $x + y \leq 10$

Q: When solving a linear programming problem graphically, what is the significance of the intersection points of the boundary lines?

They are the corner points where the maximum or minimum may occur.

Q: Which of the following best describes a feasible region in a linear programming problem?

The set of all points that satisfy all constraints.

Q: Which of the following is true about the solution set to a system of linear inequalities?

It is the set of all points that simultaneously satisfy all inequalities.

Question 1

Which of the following best describes the objective function in a linear programming problem?

Accepted Answer

It is the function being optimized, either maximized or minimized.

Question 2

A food truck sells two types of sandwiches: Plain Jaine and Sloppy Goodness. The Plain Jaine uses 1 serving of peanut butter and 1 serving of strawberry jelly. The Sloppy Goodness uses 2 servings of peanut butter and 3 servings of strawberry jelly. If the truck has 148 servings of peanut butter and 149 servings of strawberry jelly, which constraint correctly models the peanut butter limitation?

Accepted Answer

$x + 2y \leq 148$

Question 3

Which of the following is NOT a step in setting up a linear programming problem?

Accepted Answer

Graph the solution set for the objective function.

Question 4

Given the system of inequalities $x + 3y \leq 15$, $-2x + 4y \geq 0$, $x \geq 0$, $y \geq 0$, what is the boundary line for the first inequality?

Accepted Answer

$x + 3y = 15$

Question 5

When graphing the solution set for a strict linear inequality such as $3x - 4y < 12$, how should the boundary line be drawn?

Accepted Answer

As a dashed line to indicate points on the line are not included.

Question 6

A solution set to a system of linear inequalities is said to be bounded if:

Accepted Answer

The region can be completely enclosed by a circle.

Question 7

Which of the following points is a corner point for the feasible region defined by $x + y \leq 10$, $x \geq 0$, $y \geq 0$?

Accepted Answer

$(0, 10)$

Question 8

In the context of linear programming, what does a non-negativity constraint ensure?

Accepted Answer

Variables must be greater than or equal to zero.

Question 9

Suppose you are maximizing $P = 2x + 3y$ subject to $x + y \leq 10$, $x \geq 0$, $y \geq 0$. Which method would you use to find the maximum value?

Accepted Answer

Method of Corners

Question 10

If the feasible region for a linear programming problem is unbounded, which of the following statements is true?

Accepted Answer

The region cannot be completely enclosed by a circle.

Question 11

Which of the following systems of inequalities would produce a feasible region that is a triangle in the first quadrant?

Accepted Answer

$x \geq 0$, $y \geq 0$, $x + y \leq 10$

Question 12

When solving a linear programming problem graphically, what is the significance of the intersection points of the boundary lines?

Accepted Answer

They are the corner points where the maximum or minimum may occur.

Question 13

Given the constraints $x + 2y \leq 8$ and $x \geq 0$, $y \geq 0$, which test point would you use to determine which side of the boundary line $x + 2y = 8$ to shade?

Accepted Answer

$(0, 0)$

Question 14

A company wants to minimize cost $C = 5x + 7y$ subject to $x + y \geq 12$, $x \geq 0$, $y \geq 0$. Which of the following is a valid constraint for this problem?

Accepted Answer

$x + y \geq 12$

Question 15

Which of the following best describes a feasible region in a linear programming problem?

Accepted Answer

The set of all points that satisfy all constraints.

Question 16

If you have the constraints $x \geq 0$, $y \geq 0$, and $x + y \leq 5$, which of the following points is NOT in the feasible region?

Accepted Answer

$(3, 3)$

Question 17

Which of the following is true about the solution set to a system of linear inequalities?

Accepted Answer

It is the set of all points that simultaneously satisfy all inequalities.

Question 18

When graphing $y \leq 2x + 3$, which side of the boundary line should be shaded?

Accepted Answer

The side below the line $y = 2x + 3$

Question 19

Which of the following is a correct way to write a non-strict linear inequality for use in a linear programming problem?

Accepted Answer

$2x + 3y \geq 18$

Linear Programming and Systems of Linear Inequalities: Business Calculus Study Notes

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