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- Suppose the total flow into a node of a network isrestricted to 10 units or less. How can we represent thisrestriction via an arc capacity constraint? (This still allowsus to use the Ford–Fulkerson method to find the maximumflow.)We are in a M/M/1/3 queueing system in which we wish to determine the cost of operating the system. Each customer in the queue costs us $100 per hour and each customer being served costs us $50 an hour. Customers arrive at a rate of 4 per hour and the server can serve customers at a rate of 5 per hour. The following table in the picture provides Pn values, W, and Wq:I need help with the constraint and how to solve the probelm on excel
- The Bayside Art Gallery is considering installing a video camera security system to reduce its insurance premiums. A diagram of the eight display rooms that Bayside uses for exhibitions is shown in the figure below; the openings between the rooms are numbered 1-13. A security firm proposed that two-way cameras be installed at some room openings. Each camera has the ability to monitor the two rooms between which the camera is located. For example, if a camera were located at opening number 4, rooms 1 and 4 would be covered; if a camera were located at opening 11, rooms 7 and 8 would be covered; and so on. Management decided not to locate a camera system at the entrance to the display rooms. The objective is to provide security coverage for all eight rooms using the minimum number of two-way cameras.Four doctors work in a hospital emergency room thathandles three types of patients. The time a doctor spends with each type of patient is exponentially distributed, witha mean of 15 minutes. Interarrival times for each customertype are exponential, with the average number of arrivalsper hour for each patient type being as follows: type 1, 3patients; type 2, 5 patients; type 3, 3 patients. Assume thattype 1 patients have the highest priority, and type 3 patientshave the lowest priority (no preemption is allowed). What isthe average length of time that each type of patient mustwait before seeing a doctor?The director of Burtonsville Civil Defense Agency has been ordered to draw up a disaster plan for assigning casualties to hospitals in the event of a serious earthquake. For simplicity, we will assume that causalities will occur at two points in the city and will be transported to three hospitals. It is estimated that there will be 300 casualties at point A and 200 at point B. Travel times to hospitals 1, 2, and 3 are 25, 15, and 10 minutes, respectively; from point B they are 20, 5, and 15 minutes. Hospital capacities for emergency cases are 250, 150, and 150 patients. How should the victims be assigned to hospitals to minimize the total time lost in transporting them? Disaster Point Hospital Total Casualties 1 2 3 A 25 15 10 300 B 20 5 15 200 Maximum Capacity 250 150 150 Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You…
- Search for the best solution of the following integer program using the branch and bound algorithm.Jim Jones manufactures inexpensive set-it-up-yourself furniture for students. He currently makes two products – bookcases and tables. Each bookcase contributes $24 to profit, and each table, $20. Each product passes through two manufacturing points, cutting and finishing. Bookcases take 4 hours a unit in cutting and 4 hours in finishing. Tables require 3 hours a unit in cutting and 5 in finishing. There are currently 40 hours available in cutting and 50 in finishing. Determine the optimum solution. Use graphic linear programming to find the product mix that produces the maximum profit for Jim.A company supplies goods to three customers, who eachrequire 30 units. The company has two warehouses.Warehouse 1 has 40 units available, and warehouse 2 has 30units available. The costs of shipping 1 unit from warehouseto customer are shown in Table 7. There is a penalty for eachunmet customer unit of demand: With customer 1, a penaltycost of $90 is incurred; with customer 2, $80; and withcustomer 3, $110. Formulate a balanced transportationproblem to minimize the sum of shortage and shipping costs.
- Which of the following is not an assumption of a maximum flow problem? Multiple Choice All flow through the network originates at one node, called the source. If a node is not the source or the sink then it is a transshipment node. Flow can move toward the sink and away from the sink. The maximum amount of flow through an arc is given by the capacity of the arc. The objective is to maximize the total amount of flow from the source to the sink.A steel production plant manufactures bands and coils which sell at a profit of $25 and $30 per ton,respectively. The production rate of the plant for bands is 200 tons/hr, and that for coils is 140 tons/hr.Based on the market analysis, it has been identified that the weekly demand is at most 6000 tons and4000 tons for bands and coils, respectively . The plant operates for a maximum of 40 hours per week. 1. In Microsoft Excel, formulate a linear programming model instance for this problem, then solve. 2. Assume that the products need to be painted after manufacturing, and the painting departmentcan paint at a rate of 600 tons per hour for bands and 400 tons per hour for coils. The paintingdepartment works only for 20 hours. Update the linear programming model instance to accom-modate this requirement, and re-solve the problem. 3. The plant is planning to introduce another product “rods” to its production mix with the followingparameters:•Profit/ton = $40•Production volume = 150…An emergency room (ER) at a Prisma Health Hospital has 10 total beds it can hold patients, i.e., the capacity of the queueing system of this ER is 10. Patients arrive to the ER at a rate of 5 per hour. Therefore, we have that λn = 6 for n = 0, 1, . . . , 9 and λ10 = 0 for this queueing system. A patient is seen by an ER doctor as the ‘service’ of this queueing system. The amount of time required for an ER doctor to treat a patient is exponentially distributed with a mean of .4 hours. We seek the minimum number of ER doctors so that the expected time of a patient waiting to be seen (so the Wq) is less than or equal to 15 minutes (.25 hours). You should begin by analyzing s = 1 and show any calculations that were used to determine Wq for each number of servers that you considered until you meet the target metric.