Question

Please help linear programming??

Answer 1

The equation of each line enclosing the region is a constraint.
For example y\(\ge\)0 means that the region lies above the x-axis, and so on.
The four corner points are the intersections of the lines, for example, (50,0)
or x=50, y=0 is one of the four corner points.

Answer 2

How do I find the constraints? @mathmate

Answer 3

The constraints are the equations of the lines surrounding the region. I gave one as y\(\ge\)0.
Another one lies on the y-axis, and I am sure you could find it.
The two remaining ones are the sloping lines.
You can find the equations by picking two points on each line, and finding the equation of these lines by the equation by
1. find the slope using slope=m=(y2-y1)/(x2-x1)
2. find the equation of the line using (y-y1)=m(x-x1).

Answer 4

so to get the constraints I first need the four corner points?

Answer 5

Quite correct, at least three (other than the origin).

Answer 6

So what about these questions? Can you also help me?

Answer 7

@mathmate

Answer 8

Are the two questions related?

Answer 9

I mean related to the Linear Programming problem?

Answer 10

Are the four corner points (50,0) (0,0) (0,50) (20,45) and yes the two questions are related to problem, I'm really confused.

Answer 11

Yes, you've got the four critical points.
There is a good chance these will also give you the maximum salary, i.e. one of the four points.

Answer 12

We can rule out (0,0) because it gives a zero income.

Answer 13

okay so can you help with finding the constraints because I'm really confused on how to ?

Answer 14

Can you find the slope of a line between two points?

Answer 15

The equation to be used is m=slope=\(\large\frac{y2-y1}{x2-x1}\)

Answer 16

yes which two points though?

Answer 17

Any two points on the line/constraint.
Preferably where the line cuts the intersections of the grid points so your coordinates will be exact (i.e. not estimated).

Answer 18

can I use the ones from the four corners?

Answer 19

Anyone, as long as the two points you choose both lie on the line/constraint you're trying to calculate.

Answer 20

Yes, use two of the four points that you've found, they're there anyway and you've done the work.

Answer 21

Okay so then in question c the one I posted you asked that had to do with the problem what do I do there?

Answer 22

@mathmate

Answer 23

Yes, I think a,b,c,d together all refer to the graph.

Answer 24

Can you help me with question c ?

Answer 25

Okay I'm seriously lost on how to find the four constraints?

Answer 26

I am still pondering between c and d, because they are asking for the same answer.
The maximum value is if you substitute the 4 ordered pairs into the income equation, you will find \(one\) that has the highest income. This is the answer to c or d.
BUT, if you \(two\) points with the same maximum income, then maximum income is located at both points, AND anywhere along the line joining the two points.
I think this scenario is not happening here.

Answer 27

A constraint is an equation representing the boundary of the region.
I already gave you two of the constraints, namely the lines on the left (x=0) and the one at the bottom (y=0).
The two other equations would take the form of
y=mx+b
where m=slope, b=y-intercept.
As I mentioned earlier, the slope can by found using \(\large\frac{y2-y1}{x2-x1}\).
Figure that out for one of the lines then we can proceed to the next step.

Answer 28

so is x<45 a constraints?