MATB41H3 Lecture Notes - Lecture 24: Ellipse, Bijection, Celtic F.C.

For all the problems, all of the greater thanand less than signs (>,<) should be a greater/less than equalto signs.

-Solve using the simplexmethod:

1) Maximizesubject: p= x + 2y +3z

3x + y+ 3z<1

2x + y + z<2

x> 0, y> 0, z >0

-Solve using the simplexmethod:

2) Minimize subject to: c=10s + 3t,

5s + 4t > 4

2s + 3t > 2

s> 0, t> 0

-Solve:

3)Maximizesubject to P = 3x+ 2y + z

2x + 3y + z <30

x - 2y + z > 20

2x + 5y + 2z >0

x > 0, y > 0, z >0

F(x,y,z) = <0,cos(xz),-sin(xy)> Find curl F

Compute the Jacobian [d(x,y,z)] / [d(?,?,?)] for thetransformation from Cartesian coordinates to sphericalcoordinates