Question

The constraints of a problem are listed below. What are the vertices of the feasible region? 4x+3y<-12, 2x+6y<-15,x>-0,y>-0

Answer 1

we will draw the graph according to the given  constraints

NOTE: when we draw the graph from constraints inequalities becomes equalities just to draw the graph

Given constraints are:

$4x+3y\leq12$

$2x+6y\leq 15$

$x\geq0$

$y\geq0$

Now we draw the graph of given constraints using graphing calculator. Please see the attachment for the graph. Shaded region is the feasible region

Answer 2

Answer:

The vertices of the feasible region are (0,0), (3,0), (1.5,2) and (0,2.5).

Step-by-step explanation:

The constraints of the problem are given by,

$4x+3y\leq 12$

$2x+6y\leq 15$

$x\geq 0$

$y\geq 0$

Zero Test states that after substituting the point (0,0) in the inequalities,

If the result is true, then the solution region is towards the origin

If the result is false, then the solution region is away from the origin.

So, puttin g(0,) in the constraints gives,

$4x+3y\leq 12[/tex implies 0 ≤ 12, which is true.[tex]2x+6y\leq 15$ implies 0 ≤ 15, which is true.

$x\geq 0$ implies 0 ≥ 0, which is true.

$y\geq 0$ implies 0 ≥ 0, which is true.

Thus, all the inequalities will have solution region towards the origin.

So, the feasible region is given as below.

Hence, the vertices of the feasible region are (0,0), (3,0), (1.5,2) and (0,2.5).