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- The figure below shows the nodes (A−I) and capacities (labelled on arcs in TB/s) of a computer network. The firm would like to know how much information can flow from node A to node I. Which nodes are the sink and source for this problem? Multiple Choice: Node A is the source, Node I is the sink. Node A is the sink, Node B is the source. Node A is the sink, Node I is the source. Node B is the sink, Node I is the source. Node B is the source, Node I is the sink.Suppose a network contains a finite number of arcs andthe capacity of each arc is an integer. Explain why theFord–Fulkerson method will find the maximum flow in thefinite number of steps. Also show that the maximum flowfrom source to sink will be an integer.ou are given a linear programming problem. Maximize P = 3x + 3y subject to 5x + 3y ≤ 30 Resource 1 2x + 3y ≤ 21 Resource 2 x ≤ 4 Resource 3 y ≥ 0 x ≥ 0 (a) Use the method of corners to solve the problem. The maximum is P = at (x, y) = . (b) Suppose P = cx + 3y. Find the range of values that the coefficient c of x can assume without changing the optimal solution. ≤ c ≤ (c) Find the range of values that Resource 1 can assume. ≤ (Resource 1) ≤ (d) Find the shadow price for Resource 1.
- Four workers are available to perform jobs 1–4.Unfortunately, three workers can do only certain jobs:worker 1, only job 1; worker 2, only jobs 1 and 2; worker3, only job 2; worker 4, any job. Draw the network for themaximum-flow problem that can be used to determinewhether all jobs can be assigned to a suitable worker.Consider the following linear programming model: maximize Z = 3x1 + 2x2 subject to : x1 +x2 ≤ 1 x1 + x2 ≥ 2 x1,x2 ≥ 0 a) Write this model in a standard (augmented) form. (i.e. Introduce slack/surplus, artificial etc.)b) Constract the initial simplex tableau and carry on your calculations to solve this model using the simplex method. Interpret your result.Solve the linear programming problem by the method of corners. Minimize C = 6x + 7y subject to 4x + y ≥ 42 2x + y ≥ 30 x + 3y ≥ 30 x ≥ 0, y ≥ 0 The minimum is C = at (x, y) =
- Solve the following Linear Programming model using the graphical method (USING EXCEL){Write the steps of construction} Q1)MaximizeH = x + 3y Objective functionsubject tox + y ≤ 502x + y ≤ 60 x ≥ 0, y ≥ 0(b) A company produces 3 products A, B and C processed on 3 machines P, Q, R before completion. Machine P can process 25 units of A or 50 unit of B or 75 units of C per hour. Machine Q can process 50 units of any of the products per hour. Machine R can process 50 units of A or 25 unit of B or 100 units of C per hour. The processing hours available on machines P, Q and R are 12, 12 and 13 respectively. Use matrix method, find (i) How many units of each of the three products can be produced per day (ii) The production cost per unit, if cost per hour of operating machines A,B and C are N$500, N$1,000 and N$1,500 respectively. (iii) The total cost of production.1. The following diagram represents a flow network. Each edge is labeled with its capacity, the maximum amount of stuff that it can carry. a. Formulate an algebraic model for this problem as a maximum flow problem. b. Develop a spreadsheet model and solve this problem. What is the optimal flow plan for this network? What is the optimal flow through the network?
- 4.Problem in the Image Please solve with the long anlysis explain and clearlydo not need to solve thr problem, jsit crrate the linear program.3. George Heinrich Printing Company wants to schedule the following seven jobs where each job must be processed by two machines A and B, first on machine A and then machine B. The processing times at machine A and B are as follows: Job i 1 2 3 4 5 6 7Processing time on machine A (ai) 15 7 4 7 10 4 7Processing time on machine B (bi) 3 9 10 6 9 5 8 (a) Suppose the inter-arrival times between jobs can be treated as zero and Johnson’srule is used to sequence and process the jobs, what is the completion time of eachjob and what is the total throughput time (makespan) of all jobs? (b) Now suppose that FIFO system (i. e., schedule job l before job 2, etc.) of schedulingand processing the jobs is used. What is the completion time of each job and whatis the total throughput time (makespan) of all jobs? (c) What would be the difference in the average time a job spends in the shop in (a)and (b) above?