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

The maximum value of Z = 3x+ 4y subjected to the constrains x+ y≤ 40,x+ 2y≤ 60, x≥ 0 and y≥ 0 is

• 120 A
• 100 B
• 140 C
• 160 D

3x + 4 > 0 is

• equation A
• identity B
• inequality 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

If x < y, 2x = A, and 2y = B, then

• A = B A
• A < B B
• A < x C
• B < y 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

2x + 3y > 4 is a linear inequality in

• one variable A
• two variables B
• three variables C
• none of these 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

x = ________ is in the solution of 2x - 3 < 0

• 2 A
• -2 B
• 3 C
• 4 D

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

• 2x + y > 8 A
• 2x + y < 6 B
• 2x - y > 1 C
• 2x + 3y < 2 D

3x + 4 < 0 is

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

The set of ordered pairs (x,y) such that ax+ by < c, and (x,y) such that ax + by>0, are called

• Half planes A
• Boundary B
• Linear Inequalities C
• Feasible regions D

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

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

ax + by < c is linear inequality in

• four variables A
• three variables B
• two variables C
• one variable D

The graph of linear equation 2x + 3y = 10

• Parabola A
• Circle B
• Hyperbola C
• Straight line D

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

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

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

A point (x,y) which satisfy a linear inequality in two variables form its

• Solution A
• Domain B
• Range C
• None D

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

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

A point where two of its boundary lines intersect is called

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

Each point of the feasible region is called

• Solution A
• feasible solution B
• Both a & b C
• None D

The point ________ is in the solution of the inequality 2x - 3y < 4

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

For graphing a linear inequality, solid line is drawn if the inequality involves the symbols:

• > or < A
• > or < B
• = or≠ C
• = or > 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

The point (1,3) is one solution of

• 3x + 5y > 29 A
• 3x + 5y < 7 B
• x + 2y < 4 C
• x + 4y > 3 D

Corner point of the system x - y≤ 2,x + y≤ 4,2x -y≤ 6,x≥ 0,y≥ 0

• (1,4) A
• (4,2) B
• (3,1) C
• (4,1) D

The point ________ is in the solution of the inequality 2x - 3y > 5

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

3x + 4 = 0 is

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