A high-speed train operator schedules six trains per day departing from City A. The destination of each train may be City B, City C, or City D. The following table shows the contribution to the high-speed operator's profit from any given number of daily trains from City A to each possible destination. Find the optimal number of trains that should depart City A for each destination. How would the answer changes if the train operator were restricted to only four daily trains? Profit per train (S) Destination Number of trains 3. 6. City B 80 150 210 250 270 280
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- A new stadium complex is being planned for Denver, and the Denver traffic engineer is attempting to determine whether the city streets between the stadium complex and the interstate highway can accommodate the expected flow of 21,000 cars after each game. The various traffic arteries between the stadium (node 1) and the interstate (node 8) are shown in the following 1 10 8 7 0 1 LO 5 0 N 3 3 4 CO 6 6 LO 5 4 5 0 0 0 2 LO 6 26 2 7 8 4 9 0 0 8 The flow capacities on each street are determined by the number of available lanes, the use of traffic police and lights, and whether any lanes can be opened or closed in either direction. The flow capacities are given in thousands of cars. Determine the maximum traffic flow the streets can accommodate and the amount of traffic along each street. Will the streets be able to handle the expected flow after a game? Hint: I would use LP to solve it.The MidLands Trucking Company based in Louisvillehas eight trucks located throughout the Mideast that havedelivered their loads and are available for shipments. Through their Internet logistics site MidLands has re-ceived shipping requests from 12 customers. The follow-ing table shows the mileage for a truck to travel to a customer location, pick up the load, and deliver it. Determine the optimal assignment of trucks to customersthat will minimize the total mileage. Customers Truck A B C D E F G H I J K L1 500 730 620 410 550 600 390 480 670 710 440 5902 900 570 820 770 910 660 650 780 840 950 590 6703 630 660 750 540 680 750 810 560 710 1200 490 6504 870 1200 810 670 710 820 1200 630 700 900 540 6205 950 910 740 810 630 590 930 650 840 930 460 5606 1100 860 800 590 570 550 780 610 1300 840 550 7907 610 710 910 550 810 730 910 720 850 760 580 6308 560 690 660 640 720 670 830 690 880 1000 710 680The following network describes a transportation scenario in which there are four sources A, B, C, and D, and three destinations P, Q, and R. (The numbers next to each arrow represent the cost of transporting one unit from that particular source to the destination located at the other end of that arrow). Write the mathematical formulation of the problem. Use the Excel Solver to solve the problem. Generate the answer and sensitivity reports in Excel, and submit your Excel workbook as a separate attachment. Provide the solution obtained in the space provided. What is the optimal cost of transportation?
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- A city is considering building a bridge across a river that runs through the city. Currently, 1.5 million people have to drive around the river for 1 hour to get to the other side of the city. There have been complaints about congestion and pollution on the road. The new bridge will cut commuter time by half. It is expected that 1 million commuters will use the bridge on a daily basis, increasing to 2 million in the next 10 years.The new bridge will cost $80 million to build. A consultant has been hired to construct the bridge and will be able to high 40 employees on full time basis to complete the construction over one year. The city will spend $100,000 to maintain the bridge every year. The city is planning to charge a toll of $2 per trip for the use of the bridge. The new bridge is also expected to reduce congestion on the current road. How will you quantify and monetize all your identified Costs Benefits What time frame will you use and why? With the following criteria,…Three refineries send gasoline to two distribution terminals through a pipeline network. Any demand that cannot be satisfied through the network is met from other sources. The pipeline network is served by three pumping stations as shown below. The capacity of each pipe segment (in million barrels per day) is shown on the arcs. Determine the optimal daily demand at each terminal that matches the maximum capacity of the network. Show your step-by-step solution and provide an organized summary at the end.eCabs is a newly created taxi service company that provides online booking for clients in the Lusaka province. eCabs has considered developing a simple website for an online booking System with the capability to enable clients access from their mobile devices and to book for a trip. At the time of their first booking, clients should be able to enter their details into an online form, along with their credit card details. However, clients can also have an account with eCabs and for any subsequent bookings, they can log in to their own account and make a booking for a taxi. They need to be able to enter their trip origin and destination. The system will give them an estimate of cost according to their trip description. Assuming you have been assigned to design and develop the system for eCabs. You are given three weeks to come up with a blueprint of the system design and present the design to a team of consultants. The online booking System should be able to perform a number of…