4 Math to Linear Programs (a) The following is a piecewise convex function: f(x) = 1-x+1 - 3x +2 + 2. 8 if x 5. Write a linear program to find a value of x which minimizes f(2). (You do not need to solve your linear program.) (b) The following three lines do not have a common point of intersection: y=-+*+ 4 y= -x-2 We want to find a point which comes close to being on all three lines. Write a linear program to find a point (3*,y*) such that the sum of the vertical distances from (2*,y*) to each line is minimized. Vertical distance is the distance from (x*,y*) to the point on the line with x- coordinate x*. (You do not need to solve your linear program.) 4 Math to Linear Programs (a) The following is a piecewise convex function: f(x) = 1-x+1 - 3x +2 + 2. 8 if x 5. Write a linear program to find a value of x which minimizes f(2). (You do not need to solve your linear program.) (b) The following three lines do not have a common point of intersection: y=-+*+ 4 y= -x-2 We want to find a point which comes close to being on all three lines. Write a linear program to find a point (3*,y*) such that the sum of the vertical distances from (2*,y*) to each line is minimized. Vertical distance is the distance from (x*,y*) to the point on the line with x- coordinate x*. (You do not need to solve your linear program.)