Theory (60 points) 1. This is a tableau for transport problem. (20 points) Problem #1: please refer to the code on lecture page 14. For part b in problem #1, please see the attached figure and start...

Please see instructions for this assignment in the word document, complete both theory and practice parts in a ipynb file.


Theory (60 points) 1. This is a tableau for transport problem. (20 points) Problem #1: please refer to the code on lecture page 14. For part b in problem #1, please see the attached figure and start with this table below 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) Problem #2: please refer to the code on lecture page 36. 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) problem #3: please solve the problem on page 29. value of information data 220 fall 2020 week 10 class will be started at 6:00 pm. please mute your microphone! you can turn off your camera if you want. please use the zoom chat (instead of a microphone) if you have a question. lecture 9: linear programing and operations research dr. seungjoon (joon) lee data 220: mathematical methods for data analytics operations research why do we learn linear programing why do we learn linear programing lp example giapetto’s, inc., manufactures wooden soldiers and trains. each soldier built: sell for $27 and uses $10 worth of raw materials. increase giapetto’s variable labor/overhead costs by $14. requires 2 hours of finishing labor. requires 1 hour of carpentry labor. each train built: sell for $21 and used $9 worth of raw materials. increases giapetto’s variable labor/overhead costs by $10. requires 1 hour of finishing labor. requires 1 hour of carpentry labor. each week giapetto can obtain: all needed raw material. only 100 finishing hours. only 80 carpentry hours. demand for the trains is unlimited. at most 40 soldiers are bought each week. giapetto wants to maximize weekly profit (revenues – costs). formulate a mathematical model of giapetto’s situation that can be used maximize weekly profit. linear programing linear programing linear programing linear programing linear programing linear programing linear programing linear programing linear programing linear programing linear programing transport equation $ 7 $ 8 $ 10 $ 11 $ 9 $ 8 200 500 300 200 200 transport equation transport equation transport equation transport equation balanced and different cost 2 3 5 6 5 2 1 3 5 10 3 8 4 6 15 12 8 4 6 transport equation balanced and different cost 2 3 5 6 5 2 1 3 5 10 3 8 4 6 15 12 8 4 6 transport equation balanced and different cost 2 3 5 6 5 2 1 3 5 2 3 8 4 6 15 12 0 4 6 8 transport equation balanced and different cost 2 3 5 6 5 2 1 3 5 0 3 8 4 6 15 10 0 4 6 82 transport equation balanced and different cost 2 3 5 6 5 2 1 3 5 10 3 8 4 6 15 12 8 4 6 82 5 5 4 6 transport equation balanced and different cost 2 3 5 6 5 2 1 3 5 10 3 8 4 6 15 12 8 4 6 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 transport equation maximum cardinality bipartite matching problem dynamic programing dynamic programing dynamic programing item weight benefit 1 4 11 2 3 7 3 5 12 10 lbs. knapsack dynamic programing dynamic programing dijkstra's algorithm dijkstra's algorithm dijkstra's algorithm dijkstra's algorithm dijkstra's algorithm dynamic programing dynamic programing dynamic programing 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)="" problem="" #3:="" please="" solve="" the="" problem="" on="" page="" 29.="" value="" of="" information="" data="" 220="" fall="" 2020="" week="" 10="" class="" will="" be="" started="" at="" 6:00="" pm.="" please="" mute="" your="" microphone!="" you="" can="" turn="" off="" your="" camera="" if="" you="" want.="" please="" use="" the="" zoom="" chat="" (instead="" of="" a="" microphone)="" if="" you="" have="" a="" question.="" lecture="" 9:="" linear="" programing="" and="" operations="" research="" dr.="" seungjoon="" (joon)="" lee="" data="" 220:="" mathematical="" methods="" for="" data="" analytics="" operations="" research="" why="" do="" we="" learn="" linear="" programing="" why="" do="" we="" learn="" linear="" programing="" lp="" example="" giapetto’s,="" inc.,="" manufactures="" wooden="" soldiers="" and="" trains.="" each="" soldier="" built:="" sell="" for="" $27="" and="" uses="" $10="" worth="" of="" raw="" materials.="" increase="" giapetto’s="" variable="" labor/overhead="" costs="" by="" $14.="" requires="" 2="" hours="" of="" finishing="" labor.="" requires="" 1="" hour="" of="" carpentry="" labor.="" each="" train="" built:="" sell="" for="" $21="" and="" used="" $9="" worth="" of="" raw="" materials.="" increases="" giapetto’s="" variable="" labor/overhead="" costs="" by="" $10.="" requires="" 1="" hour="" of="" finishing="" labor.="" requires="" 1="" hour="" of="" carpentry="" labor.="" each="" week="" giapetto="" can="" obtain:="" all="" needed="" raw="" material.="" only="" 100="" finishing="" hours.="" only="" 80="" carpentry="" hours.="" demand="" for="" the="" trains="" is="" unlimited.="" at="" most="" 40="" soldiers="" are="" bought="" each="" week.="" giapetto="" wants="" to="" maximize="" weekly="" profit="" (revenues="" –="" costs).="" formulate="" a="" mathematical="" model="" of="" giapetto’s="" situation="" that="" can="" be="" used="" maximize="" weekly="" profit.="" linear="" programing="" linear="" programing="" linear="" programing="" linear="" programing="" linear="" programing="" linear="" programing="" linear="" programing="" linear="" programing="" linear="" programing="" linear="" programing="" linear="" programing="" transport="" equation="" $="" 7="" $="" 8="" $="" 10="" $="" 11="" $="" 9="" $="" 8="" 200="" 500="" 300="" 200="" 200="" transport="" equation="" transport="" equation="" transport="" equation="" transport="" equation="" balanced="" and="" different="" cost="" 2="" 3="" 5="" 6="" 5="" 2="" 1="" 3="" 5="" 10="" 3="" 8="" 4="" 6="" 15="" 12="" 8="" 4="" 6="" transport="" equation="" balanced="" and="" different="" cost="" 2="" 3="" 5="" 6="" 5="" 2="" 1="" 3="" 5="" 10="" 3="" 8="" 4="" 6="" 15="" 12="" 8="" 4="" 6="" transport="" equation="" balanced="" and="" different="" cost="" 2="" 3="" 5="" 6="" 5="" 2="" 1="" 3="" 5="" 2="" 3="" 8="" 4="" 6="" 15="" 12="" 0="" 4="" 6="" 8="" transport="" equation="" balanced="" and="" different="" cost="" 2="" 3="" 5="" 6="" 5="" 2="" 1="" 3="" 5="" 0="" 3="" 8="" 4="" 6="" 15="" 10="" 0="" 4="" 6="" 82="" transport="" equation="" balanced="" and="" different="" cost="" 2="" 3="" 5="" 6="" 5="" 2="" 1="" 3="" 5="" 10="" 3="" 8="" 4="" 6="" 15="" 12="" 8="" 4="" 6="" 82="" 5="" 5="" 4="" 6="" transport="" equation="" balanced="" and="" different="" cost="" 2="" 3="" 5="" 6="" 5="" 2="" 1="" 3="" 5="" 10="" 3="" 8="" 4="" 6="" 15="" 12="" 8="" 4="" 6="" x1="" x2="" x3="" x4="" x5="" x6="" x7="" x8="" x9="" x10="" x11="" x12="" transport="" equation="" maximum="" cardinality="" bipartite="" matching="" problem="" dynamic="" programing="" dynamic="" programing="" dynamic="" programing="" item="" weight="" benefit="" 1="" 4="" 11="" 2="" 3="" 7="" 3="" 5="" 12="" 10="" lbs.="" knapsack="" dynamic="" programing="" dynamic="" programing="" dijkstra's="" algorithm="" dijkstra's="" algorithm="" dijkstra's="" algorithm="" dijkstra's="" algorithm="" dijkstra's="" algorithm="" dynamic="" programing="" dynamic="" programing="" dynamic="">