6.A pipeline is to be built that willlink six cities. The cost (in hundreds ofmillions of Yuan) of constructing eachpotential link is shown in the weighted graph.Find a system of pipelines to connect all thecities and yet minimize the total cost.(1)Show the system of pipelines.Give the minimum total cost.(2)A.19C'2529121516F1722D1118E

Given map: To show: System of pipeline minimal cost

Answered: A pipeline is to be built that will…

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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Draw a network showing the quantities obtained in the final iteration and the optimal value of z.
Assuming an M/M/1 system setup with a service rate of 25 entities per hour and an idling ratioof 4% Define the system’s birth rate. Define at least two ways of arriving at the number of entities in the system. Define the ratio of the time an entity spends waiting and the time the entity spends in thesystem?
A piece of wire of length 58 is cut, and the resulting two pieces are formed to make a circle and a square. Where should the wire be cut to (a) minimize and (b) maximize the combined area of the circle and the square?
3.4 The system is tested on a sample of one hundred computers and the average connection speed is found to be far below 400 kilobits. What hypothesis should probably be rejected? Explain. If the customer needs a connection speed of 400 kilobits to run her application programs, what is the business decision that corresponds to the decision regarding the hypotheses?
A certain closed economy consists of two sectors: goods and services.Suppose that 60% of all goods and 30% of all services. are used in theproduction of goods. What proportion of the total economic output is usedin the production of goods?
The Operations Manager of a construction company wants to assign four contractors to four jobs in such a way as to minimize the time taken to complete four buildings of a special kind and size. Based on experience, the times taken (in months) for each contractor to complete each job are given in the table below. Jobs Contractor 1 2 3 4 1 15 15 16 14 2 20 18 16 19 3 24 26 24 23 4 30 35 38 25 Required:- Using the Hungarian (manual) method, determine the optimal assignment of contractors to jobs in order to minimize the total time taken to complete the jobs. Indicate this overall time and show all working. 2. Write an LP formulation that could be used to solve this problem with the relevant LP software packages.
A line of LRT with five (5) stations will be constructed in a city. A forecast passenger demand is given below: Depart Station Boarding Station 1 2 3 4 5 1 0 1600 10000 2000 250 2 230 0 11000 2071 230 3 60 1400 0 1500 170 4 250 1700 10400 0 250 5 300 1900 12000 2500 0 (a) Compute the number of passengers between each pair of the stations for both directions.(b) In this LRT project, headway must not be less than 120 seconds and must not be greater than 300 seconds. All stations are designed to cater a train of 6 couches. The capacity of each couch is 280 passengers. Based on the computed maximum passengers in (a), compute headway possibilities and corresponding number of couches per train. You may use rail utilisation factor of 0.75 and load factor of 0.9.
Assume that each full team consists of 1 doctor and 5 nurses, and that each half team consists of 1 doctor and 3 nurses. Assume also that there are 220 doctors and 920 nurses available to serve on teams. Assume also that the each full team can inoculate 240 people per hour and that each half team can inoculate 140 people per hour. How many full teams and half teams should be formed in order to maximize the number of inoculations per hour?
A firm has 2 plants with different functions: - Plant 1: MC = 30 + Q - Plant 2: MC = 20 + 2Q How to allocation output between the 2 plants to minimize total cost of producing 50 units of output? What is the minimum total cost?
A rectangular vault is to be constructed on an existing floor at a bank so as to enclose avolume of 485 cubic meters. The cost per square meter of materials is $2,000 for the ceiling,$9,000 for the wall with the door and $3,000 for the other three walls. The minimized costof the vault rounded to the nearest $1,000 dollars is:a. $964,000b. $971,000c. $982,000d. $993,000
A piece of wire of length 60 is cut, and the resulting two pieces are formed to make a circle and square. What should the wire be cut to (a) maximize and (b) minimize the combined area of the circle and the square?
A restaurant requires different numbers of full-time employees on different days of the week.Union rules state that each full-time employee must five consecutive days and then two daysoff. The management office wants to meet its daily requirements (Monday: 11, Tuesday: 16,Wednesday: 14, Thursday: 15, Friday: 18, Saturday: 19 and Sunday: 23) using only full-timeemployees. Formulate an LP that the restaurant can use to minimize the number of full timeemployees who must be hired

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