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- Find the initial basic feasible solution for the following transportation problem using VAM. Explaineach step.Ram ,mohan and sohan took loan of RS.x,y and z on rate of intrest r%,p%,q% for time t1,t2 and t3 years respectively.calculate simple intrest they will pay and find who will pay the most using ternary operator?A contractor owns three excavators of different capacity. He/she wants to dispatch these excavatorsinto three different jobs. The performance of the excavators is measured as the time consumed toperform each job. The data of the time tests are shown as given in the table below. (a) Draw a network flow diagram.(b) Formulate a mathematical model to obtain the minimum time.(c) Solve this model using the Vogel’s approximation model.
- Consider the dual of a minimum cost network flow problem in which the costs are integer. Prove that the basic feasible solutions are integer.Please extract this tabular form using the least cost method Part 4-Network Problems(10)The U.S. government is auctioning off oil leases at two sites: 1 and 2. At each site, 100 000 acres of land are to be auctioned. Cliff Ewing, BlakeBarnes, and Alexis Pickens are bidding for the oil. Governmentrules state that no bidder can receive more than 40% of the land being auctioned. Cliff has bid $1,000/acre for site 1 land and $2,000/acre for site 2 land. Blake has bid $900/acre for site 1 land and $2,200/acre for site2 land. Alexis has bid $1,100/acrefor site 1 land and$1,900/acre for site 2 land. Formulate a balanced transportation model to maximize the government’s revenue.The city of Smallville consists of five subdivisions, Mayor Takeda wants to build telephone lines to ensure that all subdivisions can communicate with each other. The distances between the subdivisions are given in the figure below: Assume that no telephone line can be built between subdivisions 1 and 4. ______ 1) What is the minimum length of cable required? 12 units b. 14 units c. 15 units d. 16 units ______ 2) Which arcs should be connected to obtain the least cable wires needed? (1, 3), (3, 5), (3, 4), (3, 2) c. (1, 5), (5, 3), (3, 4), (3, 2) (1, 3), (3, 5), (5, 4), (4, 2) d. (1, 2), (2, 4), (4, 3), (3, 5) ______ 3) What would be the total length if the following arcs are connected: (1, 3), (3, 4), (4, 5), (3, 2) 18 units b. 17 units c. 15 units d. 16 units