The network below represents alternative routings to drive from Point 1 to Point 6. Formulate theproblem as a shortest distance problem.6.FromТоMiles141446.1What is the objective function for this model?O MIN X61MIN 4X12 + 3X13 +5X34 + 4X35 + 4X24 + X46 + 2X56 + X61MIN X12 + X13MIN 4X12 + 3X13 + 5X34 + 4X35 + 4X24 + X46 + 2X5613

The shortest path problem is the problem of finding a path between two vertices (or nodes) in a…

Answered: The network below represents…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A manufacturer of refrigerators must ship at least 100 refrigerators to its two warehouses. Each warehouse holds a maximum of 100 refrigerators. Warehouse A holds 40 refrigerators already, while warehouse B has 15 on hand. It costs $10 to ship a refrigerator to warehouse A and $14 to ship one to warehouse B. How many refrigerators should be shipped to each warehouse to minimize cost? Find the objective function and the constraints for the above problem.
Please show and explain how to do each step to solve this problem.
A farmer has 800 meters of fencing and needs to fence off a rectangular paddock that borders a straight river. He doesn't need to fence along the river. Set up and solve an appropriate optimisation problem to find the dimensions of the paddock that has the largest area.
Part1)An airplane carries water and medical kits to survivors of a natural disaster. The plane can carry a maximum payload of 80,000 pounds. Each container of water weighs 20 pounds, and each medical kit weighs 10 pounds.The cargo space holds a maximum of 6000 cubic feet of cargo. Graph these constraints on the grid provided, and write some units on the axes. Assume each container has a volume of 1 cubic foot. Part2)If each container of water serves 10 people and each medical kit aids 6 people, find the number of water containers and medical kits that could help the most people
Explain how the various changes to LP affect the optimal solution. a) Changes to the objective function coefficient b) Changes to the RHS of a constraint
Imagine you are in a city that has a grid of streets with perfectly square blocks and that the only way to get from one intersection to another is to follow the block system. How many blocks will you have to walk (or pay the cabdriver for) if you want to get from the intersection of 10th Ave and 25th Street to the intersection of 6th Ave and 28th Street? If you had a jet pack and could fly over the buildings, how many blocks in length would the shortest path be? How does this compare to #1? (Hint: Pythagorean Theorem)
Farmer Brown wants to upgrade the fencing around his rectanger pasture. He would like to put a stone fence along one(1) side and a wooden fence along the other three (3) sides. The cost of the stone fence is $100 per linear foot, and the cost of the wooden fence is $20 per linear foot. a. If the pasture must have an area of 7,500 square feet, what are the dimensions of the field which will minimize the cost of the fencing? What will the cost of the fencing be at the dimensions that you found?

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