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# Area bounded by three lines

Posted 11 years ago
 Hi, optimization, area of functionI 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 = 700Can 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
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Posted 11 years ago
 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 sidespoint2-point1 point3-point1Finally, use cross product to find the result: (1/2*Cross[point2-point1, point3-point1])[[3]]
Posted 11 years ago
 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}])