just need help with question 7 please

Consider the following optimization problem. max 1023g; i + 0, Vi= 1,...,3 1. (10 points) Write the problem in standard form using matrices. Report all the entries and dimensions of A, B, X, and c. 2. (10 points) Without making any calculation, provide arguments to show that the point (2,...,13)' = 0 is an extreme point. 3. (10 points) Determine the maximum number of basic solutions that you may encounter in this problem. 4. (15 points) Using algebra, enumerate all the extreme points and plot them in a 3D graph with axes 21, 22, and 13. 5. Find all the extreme directions of the feasible region. Proceed as follows. (a) (10 points) Provide the mathematical formulation needed to find the recession cone. (b) (10 points) Using algebra, enumerate all the extreme points of the problem with constraints from Part 5a and an additional constraint to "close" the recession cone. Use K = 2. What can you conclude about the extreme directions? (c) (5 points) Using the results from Part 5b, determine whether the feasible region of the initial problem is bounded. 6. (10 points) Find the basis corresponding to the point with coordinates (21, 22, 23) = (0,0,10000). 7. (15 points) Determine whether the point from Part 6 is optimal. Use the reduced costs. Consider the following optimization problem. max 1023g; i + 0, Vi= 1,...,3 1. (10 points) Write the problem in standard form using matrices. Report all the entries and dimensions of A, B, X, and c. 2. (10 points) Without making any calculation, provide arguments to show that the point (2,...,13)' = 0 is an extreme point. 3. (10 points) Determine the maximum number of basic solutions that you may encounter in this problem. 4. (15 points) Using algebra, enumerate all the extreme points and plot them in a 3D graph with axes 21, 22, and 13. 5. Find all the extreme directions of the feasible region. Proceed as follows. (a) (10 points) Provide the mathematical formulation needed to find the recession cone. (b) (10 points) Using algebra, enumerate all the extreme points of the problem with constraints from Part 5a and an additional constraint to "close" the recession cone. Use K = 2. What can you conclude about the extreme directions? (c) (5 points) Using the results from Part 5b, determine whether the feasible region of the initial problem is bounded. 6. (10 points) Find the basis corresponding to the point with coordinates (21, 22, 23) = (0,0,10000). 7. (15 points) Determine whether the point from Part 6 is optimal. Use the reduced costs