ECAT (Pre-Eng) Mathematics Chapter 21 Linear Inequalities & Linear Programming

The points (x, y) which satisfy a linear inequality in two variables x and y from its

• domain A
• range B
• solution C
• none of these D

• p < r A
• p > rr B
• p + r < 0 C
• p - r < 0 D

x = ________ is in the solution of 2x + 3 > 0

• 1 A
• -2 B
• -3 C
• -4 D

If -1 < x < 0, which of the following statements must be true?

• x < x²< x³ A
• x < x³< x² B
• x²< x³< x C
• x²< x < x³ D

Which is not a half plane

• ax + by < c A
• ax + by > c B
• Both A and B C
• None D

The real numbers which satisfy an inequality form its

• solution A
• coefficient B
• domain C
• range D

Multiplying each side of an inequality by (-1) will:

• Not effect A
• Change the sign B
• Become zero C
• Not defined D

x = 1 is in the solution of the inequality

• x + 1 > 0 A
• x - 2 > 0 B
• 3x - 1 < 0 C
• x + 2 < 0 D

3x + 4 < 0 is

• inequality A
• equation B
• identity C
• not inequality D

There may be ______ feasible solution in the feasible region

• Infinite A
• Finite B
• Defined C
• None of above D

An expression involving any of the symbols <,>,< or > is called

• equation A
• inequality B
• linear equation C
• identity D

x = -1 is in the solution of the inequality

• x + 5 < 0 A
• 2x + 3 < 0 B
• x > 0 C
• 2x + 3 > 0 D

If ab > 0 and a < 0, which of the following is negative?

• b A
• -b B
• -a C
• (a - b)² D

The solution set of the inequality ax + by < c is

• straight line A
• half plane B
• parabola C
• none of these D

The corner point of the boundary lines, x-2y

2x + y = 2 is:

• (2,6) A
• (6,2) B
• (-2,2) C
• (2,-2) D

(1, 1) is the in the solution of the inequality

• 3x + 4y > 3 A
• 2x + 3y < 2 B
• 4x = 3y > 5 C
• 2c - 3y > 2 D

x = ________ is in the solution of 2x - 5 > 0

• 0 A
• 2 B
• -2 C
• 3 D

For which of the following ordered pairs (s, t) is s + t > 2 and s - t < -3?

• (3, 2) A
• (2, 3) B
• (1, 8) C
• (0, 3) D

The total cost of 2 apples and 3 oranges is $1.70, which of the following is true

• The cost of one apple A
• The cost of one orange B
• Both have equal cost per item C
• Cost of each single item can not be determined D

x is a member of the set [-1, 0, 3, 5] y is a member of the set {-2, 1, 2, 4} which is possible?

• x - y = -6 A
• x - y < -6 B
• x - y > -6 C
• None D

(1,0) is in the solution of the inequality

• 3x + 2y > 8 A
• 2x - 3y < 4 B
• 2x + 3y > 3 C
• x - 2y < -5 D

x = 0 is in the solution of the inequality

• x > 0 A
• 3x + 4 < 0 B
• x + 3 < 0 C
• x - 2 < 0 D

Optimal solution is found by evaluation the objective function at

• All point of feasible region A
• Corner point B
• Origin C
• None D

A point where two of its boundary lines intersect is called

• Corner point A
• Feasible point B
• Vertex C
• Feasible solution D

The solution set of x < 4 is

• -∞< x < 4 A
• -∞> x > 4 B
• -∞< x < 2 C
• -∞> x > 2 D

3x + 4 = 0 is

• not inequality A
• equation B
• identity C
• inequality D

(2, 1) is in the solution of the inequality

• 2x + y > 7 A
• x - y > 2 B
• 3x + 5y < 6 C
• 2x + y < 6 D

A point of a solution region where two of its boundary lines intersect, is called

• Boundary A
• Inequality B
• Half plane C
• Vertex D

The graph of y < 2 is the

• Left half plane A
• upper half plane B
• Right half plane C
• Lower half plane D

The point _________ is in the solution of the inequality 2x + 3y < 5

• (1,1) A
• (2,2) B
• (0,1) C
• (0,2) D