Inequalities in Linear Programming

The video tutorial covers reading and writing inequalities for linear programming, focusing on integer coefficients. It explains basic notation, graphing techniques, and provides examples of inequalities. The tutorial also discusses graphing feasible regions and handling complex scenarios. Finally, it contextualizes inequalities within specific problems, offering multiple ways to interpret and express them.

What does a strict inequality mean in linear programming?

• The values cannot be equal.

• The values must be greater than zero.

• The values must be less than zero.

• The values can be equal.

How is the inequality 'the number of cats must be at least half the number of dogs' represented?

• X >= 2Y

• Y = 2X

• 2Y >= X

• Y <= 2X

What is the feasible region in a graph?

• The area below all lines.

• The area where all constraints are satisfied.

• The area where no constraints are satisfied.

• The area above all lines.

How can the inequality 'the number of dogs must be less than four times the number of cats' be written with integer coefficients?

• 4X < Y

• X < 4Y

• X > 4Y

• Y < 4X

What does the inequality 'the number of dogs must be at least one-fourth of the total production' imply?

• X <= 4Y

• X + Y >= 4X

• 4X >= X + Y

• Y >= 4X

How is the inequality 'the total number of cats and dogs must be between 100 and 400' represented?

• X + Y > 400

• X + Y = 100

• X + Y < 100

• 100 < X + Y < 400

What does it mean if the number of cats is between 10% and 40% of the total production?

• Y > 0.4(X + Y)

• Y < 0.1(X + Y)

• 0.1(X + Y) <= Y <= 0.4(X + Y)

• Y = 0.1(X + Y)

How is the inequality 'for every five cats, there must be no less than six dogs' represented?

• 5X <= 6Y

• 6Y >= 5X

• 6Y <= 5X

• 5Y >= 6X

What does the inequality 'the number of cats must exceed half of the total production' imply?

• 2Y > X + Y

• 2Y < X + Y

• Y > 0.5(X + Y)

• Y < 0.5(X + Y)

How can the inequality '4X is less than Y' be interpreted in the context of the problem?

• The number of cats is less than four times the number of dogs.

• The number of dogs is less than four times the number of cats.

• The number of cats is more than four times the number of dogs.

• The number of dogs is more than four times the number of cats.