Theory (60 points) 1. This is a tableau for transport problem. (20 points) 6 7 8 10 15 80 78 15 15 5 5 a. Fill the tableau by the minimum-cost method and show total cost (show the final result and the...

Please see instructions for this assignment in the word doc. You need to complete both theory and practice parts, you can use jupyter notebook.


Theory (60 points) 1. This is a tableau for transport problem. (20 points) 6 7 8 10 15 80 78 15 15 5 5 a. Fill the tableau by the minimum-cost method and show total cost (show the final result and the calculation order). (10 points) b. If we put 15 on the green box (south-west), what is the total cost? Please fill the table again and show the total cost. (10 points) 2. This table show weights and benefits of items. If we can hold up to 13 lbs, what is the best choice to maximize the total benefit? (show all possible f3(x), f2(x), f1(x)). (20 points) Item 1 Item 2 Item 3 Weight (lb) 3 5 7 Benefit 12 25 50 Practice (40 points) 1. Using “linprog”, solve the linear problem in the lecture. (20 points) a. max x3 + x4 b. x1 + x2 + x3 + x4 = 700 c. x3 - 0.5x4 =0 d. x1 + x2 <= 450="" e.="" x2="" +="" x3=""><= 300="" f.="" x2="" +="" x3=""><= x1 + x4 2. using “unboundedknapsack” or your own module, please check the total benefit of problem 3. (20 points) 3. using “linprog”, find the optimal matching scenario for the problem in the lecture slide. (20 points) 1. problem #1: please refer to the code on page  14. for part b in problem #1, please see the attached figure and start with this table. 2. problem #2: please refer to the code on page 36. 3. problem #3: please solve the problem on page 29. x1="" +="" x4="" 2.="" using="" “unboundedknapsack”="" or="" your="" own="" module,="" please="" check="" the="" total="" benefit="" of="" problem="" 3.="" (20="" points)="" 3.="" using="" “linprog”,="" find="" the="" optimal="" matching="" scenario="" for="" the="" problem="" in="" the="" lecture="" slide.="" (20="" points)="" 1.="" problem="" #1:="" please="" refer="" to="" the="" code="" on="" page ="" 14.="" for="" part="" b="" in="" problem="" #1,="" please="" see="" the="" attached="" figure="" and="" start="" with="" this="" table.="" 2.="" problem="" #2:="" please="" refer="" to="" the="" code="" on="" page="" 36.="" 3.="" problem="" #3:="" please="" solve="" the="" problem="" on="" page="">