1. A travel company have 3 carpools that show in figure below as node 1, 2, and 7, respectively. Driver of each carpool,

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1 A Travel Company Have 3 Carpools That Show In Figure Below As Node 1 2 And 7 Respectively Driver Of Each Carpool 1 (156.2 KiB) Viewed 25 times

1. A travel company have 3 carpools that show in figure below as node 1, 2, and 7, respectively. Driver of each carpool, They agree to meet at point 10 every morning at a certain time and proceed from there to their work in a single car. The numbers on the arcs represent the travel times in minutes. 10/ 6 1 8 5 3 15 4 8 2 6 10 6 10 a. What is the fastest route for each driver to the meeting point in node 10? Hint: you must work 3 times, one of each starting node point, first if you start at node 1 to node 10, second if start at node 2 to node 10, and last if start at node 7 to node 10! Now, in first carpool, it has 6 destination cities, hence the company arranges 5 bus to fulfill the travel demand. The cost for one-way trip for each bus to each city was given in table below in dollars, M means that the cost is very high. Further, the demand and the maximum trips of each bus were also given as total demand and total supply of each city and bus, respectively below.
Source Demand 1 2 3 4 5 1 13 14 100 18 30 3 3 0 Destination 2 3 4 1 1309 264942 3 5 6 Supply 0 5 0 6 0 19 23 11 0 0 2 24 34 M -10 16 21 2 TANIES 29 18 M 5 4 5 6 b. Find the initial basis solution using Minimum Cost Method! c. Find the optimal solution using Simplex Transportation! d. If cost of bus 1 to destination 5 decrease to $15, what will happen to your optimal solution? What will happen to your optimal solution if, there are in total 6 trips need to accomplish by bus 1, and there are 5 trips need to destination 3? e. Carpool 2 want to analyse the possibility to open new route, the problem is defined below, the number on each arc indicates its cost, and node supplies are indicated by the arrows. The lower bound of each arc is zero with upper bound is infinity S 11 3 36 28 2 8 5 6 56743 -50 3 IT 20 -60
f. (a) Execute iteration-zero of the Network Simplex algorithm starting from the spanning tree solution defined by arcs T ={(1, 4); (4,2); (2, 5), (4, 3); (3,6); (6,7)}. Indicate the value of each basis and non basis variables. g. Find the optimal solution to minimize the cost using simplex network method