Determine whether the following optimization problem is a convex optimization or not. Give your reasons.

subject to , and .

Consider the following linear program:

- Sketch the feasible set.
- Solve it by geometric method.

Simulate the simplex method one step for the following LP (note that is feasible):

.

You only need to simulate one step, namely, choose some to increase and then shift the coordinates.

We would like to use two-phase simplex method to solve the following linear program.

.

The first step should be to find a feasible solution by simplex method, since is not feasible. What linear program should we solve at the first step (in order to find a feasible solution)?

(You only need to write the linear program. No need to solve it.)

Write the dual to

.

and solve it by solving its dual.

What is the dual to the following form of linear program?

.