Optimization in Finance Problem set 5
Use the simplex method to solve the following LP problems:
5.1 Maximize z = 2x1 3x2 + 4x3 subject to 4x1 + 2x2 + x3 10,
x1 x2 + x3 5, and x1 , x2 , x3 0.
5.2 Minimize z = 3x1 + 6x2 subject to 4x1 + x2 20, x1 + x2 20,

Optimization in Finance Problem set 7
Solve the following nonlinear programming problems:
7.1 Maximize x2 + 2y 2 x subject to x2 + y 2 1.
7.2 Maximize y x2 subject to y 0, y x 2 and y 2 x.
7.3 (Question 4, Summer Examination 2014)
Let f : R2 R be dened by

Optimization in Finance Problem set 8
Solve the following nonlinear programming problems:
8.1 Maximize xeyx 2ey subject to x 0 and 0 y 1 + x/2.
8.2 Maximize x2 + y 2 + z 2 subject to x 0 and x2 + 2y 2 + 3z 2 6.
1

Graphing Functions with Asymptotes
Mathematics 53
Institute of Mathematics (UP Diliman)
Lecture 3.3
For today
1
Vertical Asymptotes
2
Horizontal Asymptotes
3
Oblique Asymptotes
4
Graphing Functions with Asymptotes
5
Graph of f from the Graph of f 0
For to