# Thread: Urgent HELP needed on 3 problems!

1. ## Urgent HELP needed on 3 problems!

Hi I have real difficulties with the following three problems, any help will be appreciated.

Write a system of linear inequality that describes the shaded region:

Determine graphically the solution set for the system of inequality and indicate whether the solution is bounded or unbounded:

Solve the linear programming problem by the method of corners:

Sorry for the poor picture quality but they are made by phone

2. ## Linear programming

Hello NonMathEmatical

These are all very straightforward questions about inequalities and linear programming. Have you tried them? I Googled 'Linear Programming' with the following result. You might find something here to get you started.

3. Originally Posted by NonMathEmatical
Write a system of linear inequality that describes the shaded region:
(snip)
Since the region is above the x-axis and to the right of the y-axis, and I see no dotted-lines on the axes, two of the inequalities are
\begin{aligned}
x &\ge 0 \\
y &\ge 0
\end{aligned}

You're given two equations of lines, x + 2y = 8 and 5x + 2y = 20. Both lines are solid, and the shaded region is either to the left or below the lines. The inequality symbol you need for both is less-than-or-equal-to. So the system of inequalities is
\begin{aligned}
x &\ge 0 \\
y &\ge 0 \\
x + 2y &\le 8 \\
5x + 2y &\le 20
\end{aligned}

01

4. Grandad thank you for your replay, I just don't have time to learn everything again but the first video was good.. Starting from there I will try to make something but from now I am sure that it will be an total failure

5. Originally Posted by NonMathEmatical
I just don't have time to learn everything again...
Unfortunately, the answer to one homework exercise is not going to help much on the test, when you don't understand the underlying material (and since the questions on the test will be different).

So please make the time to learn how to set up and solve linear programming word problems.

6. In fact I don’t care about the exams because I have done them already. The previous home-works were with 35-40 problems for solving, I have done them applying the strategy called “google it and you’ll learn how to solve them” but those are incomprehensible for me. Is that so hard to understand?? It’s not laziness or not taking responsibility…!!

PS: Thank you for the link!

7. So I ended up with the following for the second problem. Now how to continue and find P?

8. And the last problem!

9. Originally Posted by NonMathEmatical
So I ended up with the following for the second problem. Now how to continue and find P?
Hint: The solution is ALWAYS contained in one of the vertices of the polygon obtained by the intersection of lines. You have to see where the value of y is maximum in these vertices.

10. Originally Posted by NonMathEmatical
And the last problem!
It's correct now try to find the vertices to find the maximum value of y

11. Originally Posted by Rachel.F
It's correct now try to find the vertices to find the maximum value of y
Like this?

12. Originally Posted by NonMathEmatical
Like this?
Yes so the solution is x=3 and y=6 because these values give the maximum value of P

13. Thank you very much Rachel, so I need to apply the same technique to find P for the second question?

15. Originally Posted by NonMathEmatical