Feasible points of $2x+2y\le 6$ and $3x+5y\le14$ first time here and sorry for the basic question
I have an online maths assignment I am almost complete, however I seem to be struggling with what the feasible coordinates are. Graphing these two inequalities I got $(0$, $2.8)$, $(0.5$, $2.5)$ and $(3$, $0)$. I know for sure that the $(3$, $0)$ is a feasible point as the next question required me to find greatest profit, and this was the one that yielded the most.
Just wondering if I have graphed incorrectly and made a mistake?
 A: 
Here is the graph. I think you can proceed now. 
A: Hint
Each inequality represents a half plane. So here, you have the intersection of two half planes. Have you drawn this region of the plane?
A: First of all, you should be careful when introducing your letters (here, $x$ and $y$), bearing in mind that it is desirable - whatever the question, even basic, especially basic, I would say - to always specify what a letter designates.
Here, as we do not have any more details:
let $x$ and $y$ be two real numbers checking simultaneously $2x+2y \leq 6$ and $3x+5y\leq 14$.
Although it is not your request, I will allow myself in addition to the answer, some precisions which could be nevertheless useful to you to benefit from the answer.
$2x+2y \leq 6$.
So, by dividing by $2$ the two members of the inequality,
$x+y \leq 3$.
In the plane $\mathbb{R}\times \mathbb{ R}=\{(\xi,\eta): \xi \in \mathbb{R} \text{ and }\eta \in \mathbb{R}\}$,
@SarGe drew the line $(D_1)$ of equation $\xi+\eta=3$
passing through $(3,0)$ and $(0,3)$.
@SarGe has also colored one of the half-planes defined by $(D_1)$, referring to your lesson.
It is the half-plane containing $(0,0)$ since $0+0 \leq 3$.
On the other hand, $3x+5y \leq 14$.
So we draw the line $(D_2)$ of equation $5\eta=14-3\xi$ or $\eta=2.8-0.6\xi$.
It passes through $(0,2.8)$ and $(\frac{14}{ 3},0)$ with $\frac{14}{ 3}\approx 4.667$.
By solving $\begin{cases} \xi+\eta=3\\3\xi+5\eta=14  \end{cases}$, you get the point $(\frac12,\frac52)$, at the intersection of $(D_1)$ and $(D_2)$. These are the points you got so your graph must be good.
So, as @mathcounterexamples.ne writes, $(x,y)$ is one of the points in the intersection of these two half-planes.
$(3,0)$ is one of these points. But with the information you provide, we can't say anything more.
