MATH 2321 Lecture 26: 2.10 Optimization

• School: Northeastern University
• Department: Mathematics
• Course: MATH 2321
• Professor: Sumi Seo

Document Summary

"minimize d" in other words, nd the point on the plane given by 2x+4-2=1 which is closest to the point (0, 1,3). Note a point minimizes d iff the point minimizes de sol. Lth end pts: (0,0) and (0, 1) (x,y) |t=2x+2y=x) ii) b: y=0, osxe1 (0,44) | e118 smud, to(x) = 2x? (011) , o smallest "blx (0,0) i i icps: t3(x) = 4x=0, x=0 =) tot no cp. 20,0) (3/8, 5;)) the i end pts: (0,0)(11,0)). (1,0) : s: x+y=1 = x=l-y, osyal. = 2-4x+2y2 +2y2-y = 4y2-5y +2 cp"s: t (y) = 8y-5= 0, y = 518, x = 318=2(318,518)) enapts: (1. 0), (0, 1) . Consider the function d(x, y, z)=n/(x-6)=(x-1)=(2-3)2 with its domain restricted to those. (x, y, z) such that 2x+y=z=!. plane in 123. Minimize d subject to the censtraint that 2x+y+z=1. "cps on (-1,1): too (y)= -150 = no cps.