这是一篇美国的线性规划数学代写

Requirement: you must write the solutions by yourself. As difffferent problems may be assigned to MATP4820 and 6610 students, you must explicitly write whether you are taking MATP4820 or 6610.

Code submission: you are required submit your source code for any coding question in LMS for verifification. In addition, include your code, if any, together with your output in one single PDF fifile.

Bonus: In addition to the bonus problems (that will be assigned occasionally), you can earn up to 5% bonus credit if you write your homework in LaTex.

Problem 1

Consider the linear program:

minimizex1,x2 − 10x1 − 12x2

s.t. x1 + 2x2 ≤ 20

2x1 + x2 ≤ 20

x1 ≥ 0, x2 ≥ 0           (1)

1. Plot the feasible region of (1) and fifind the optimal solution by graph
2. In the lecture, we wrote (1) into an equivalent standard LP. Also, we start from a basic feasible solution and perform one step of the simplex method. Continue on the basic feasible solution obtained in class and fifind the optimal solution by the simplex method.