1. Which is linear inequality of the graph below?
Y >-x +3
2. Which is linear inequality of the graph below?
Y <x +2
3. . Which is linear inequality represents the inequality x-y>1
4. graph of the inequality : x+y <2
5. Which is not a linear Inequality :
X2 -y2 =1
6. which is not an example of linear equation y2-3y-4 = 0
7. solve : 3X + 8 = 2x-2 -10
8. 3 ( x-4) = 2(3x+5) -1 x=-7
9. which has solution of (0,4)
3x+2y=8 , x-4y =-16
Quiz 2
1 What are the solution of : y>x+2 and y < -x +3
(-2,2)(-3,0)(-1,2)
2 Graph the Inequalities y>x+2 and y<-x+3
3 What are the solution: x+y <2 and x-y >1
(1,-1) (2, -1) (1,-2)
4. which of the following is the graph x+y<2 ; x-y >1
This is the darkest region on graph, a point on that region corresponds to some value of the
decision variable. FEASIBLE REGION
The ____ in a linear programming problem is the feasible solution that gives either the
maximum or the minimum value for the objective function. OPTIMAL SOLUTION
It is a statement that one quantity or expression is greater than or less than another.
INEQUALITY
Who invented the Linear Programming in 1940s as a result of a military research? George
Dantzig
What is the goal of Linear Programming? Optimize a quantity
It is a statement that two algebraic expressions are equal. EQUATION
The ________ is expressed as linear equation involving the aggregate of some unknown
quantities. OBJECTIVE FUNCTION
The ________ are expressed as linear inequalities, which are restrictions imposed on the
quantities that make up the objective function. CONSTRAINTS
Using the feasible solutions of the given graph, find the maximum value of the Objective
Function = 3x + 2y. 54
Given the graph, what are the feasible solutions?
(0,0) (0,16) (10,8) (6,18)
Using the feasible solutions of the given graph, find the minimum value of the Objective
Function = x - 4y.-29
Using the feasible solutions of the given graph, find the maximum value of the Objective
Function = 3x + 2y. 29
Given the graph, what are the feasible solutions?
(4,1) (7,4) (0,5) (3, 8)
A company produces two products, A and B. Product A takes 1 hour to produce and costs
$2 to produce. Product B takes 2 hours to produce and costs $3 to produce. The company
has 10 hours of time available and $20 available to spend on materials. The company wants
to find the number of products A and B to produce that will minimize the cost of production
and maximize profits. What is the optimal quantity of products A and B that the company
should produce?
Let x = number of product A, y = number of product B, and z = cost of production
What is the objective function of the problem?
Z= 2X =3Y
Which of the following is not a constraint?
X,Y<0
What is the optimal quantity of products A and B that the company should produce?
4. Prod A , 2 Prod B