Area bounded by three lines

Questions
, ,
1

Hi,

optimization, area of function

I have 3 linear functions that I’d like to find area for, where x is 700.
It’s about price optimization.
I would like to find the area of the 3 functions where x = 700

Can mathematica count on areas?
And is there anyone who can help me with this.

Here is the plot:

Plot [{-x + 1030, 400 - 0.1 x, -0.5 x + 1030} , {x, 0, 1600}]

best
regards

2

I’m not clear on area at a point. For example, to find the area within the space enclosed by the three lines, I would do the following, since we already know the solution where the three lines meet ( x = 700 ).

Integrate[ -x+1030,{x,0,1500}]-(
Integrate[ 400-0.1x,{x,0,700}]-Integrate[ -0.5x+1030,{x,700,1500}])
3

Another way is to use three Solve functions for find the intersection points of the set of lines. Then use cross product to pin down the area.

sol1=Solve[-x + 1030 == 400 - 0.1 x, x] (* x = 700*)
... (for other two lines)

Then extract the points with Replace + Rule combo.

point1 = {x,-x+1030 }/.sol1
...

Then you should be able to compute the vectors of two sides

point2-point1 
point3-point1

Finally, use cross product to find the result:

(1/2*Cross[point2-point1, point3-point1])[[3]]