Question

a) Consider a manufacturing cell consisting of 6 machines, located at the following points in the x-y coordinate plane: (xī.yi)-(4,1), (x2.y2)-(2,3), (x3.y3)-(3,8), (X4.y4)-(5,8). (xs,ys) (9,3), (x6,ys) (7,2) We need to find a suitable spot, (x.y), for a robot such that its arm can easily reach each of the machines. Suppose we to select (x,y) such that it minimizes the distance from all the machines in a least squares sense, i.e., it minimizes dk where dk denotes the distance of the robot from the kth machine. Find the optimal location, (X , y) b) Use the principle of linear least squares optimization to solve the following set of simultaneous linear equations: xi -x2-3.2; 2x1 +3x2 -8.3; 2x1 x2-4.4 3x1 x2-5.5 [Note: The above problem should be done manually, but you can verify your answer by using Matlab. To do this, first rewrite the above equations as AX b and then use the Matlab command, X-Alb]

Answer 1

These tea we have Ke丬

- R5 30 11万 So/ eo55 6512312 2.0 20 4-1663720) -0-2の417GYTX 5+5.697254り lo

3.2 yu 83 5.5 4r2 18 -12 AR -(-p) 18 184-114

8-2 45.1 8 15 38 (38 (45) 1833 loest 833 12 2 6

Matlab code

A=[1 -1;-2 3;2 -1;-3 1];
b=[-3.2 8.3 -4.4 5.5]';
x=A\b

Output

x =

-1.1833
1.9833