15 X 10 6 15.5 1 3 (Max Flow Problem) 2 12 3 15 4.5 5 14.5 6 5 15.5 4.5 Z Find the maximum flow from Node X to Node Z.
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- Find the minimum value of the function z=2x+2y subject to the following constraints. x≤17 y≤16 5x+2y≥42 3x+11y≥84What combination of x and y will yield the optimum for this problem? Maximize $10x + $4y, subject to (1) 5x + 3y ≤ 15 and (2) 3x + 6y ≤ 18 and (3) x, y ≥ 0.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.
- Ana is a university student with 12 hours available daily, and she wants to distribute her time betweenstudy (x) and leisure (y) activities. She wants to maximize her total enjoyment while fulfilling heruniversity obligations. Ana considers leisure to be twice (2) as enjoyable as studying, but she alsobelieves that she should spend at least twice (2) as much time studying as she does on leisure activities.Additionally, she cannot spend more than five (5) hours a day on leisure activities to ensure that she hasenough time for her university obligations. 1. How much additional enjoyment would Ana get if she had one more hour per dayavailable, so 13 instead of 12 (dual price)?2. Would Ana experience a greater level of enjoyment if she allows herself to have amaximum of six hours per day to leisure activities instead of five, while still fulfilling her universityobligations within the 12 hours available (dual price)?3. What is the allowable increase of the coefficient accompanying leisure…Don't use chatgpt, I will 5 upvotes Alan wants to bake blueberry muffins and bran muffins for the school bake sale. For a tray of blueberry muffins, Alan uses 1/3 cup of oil and 2 eggs. For a tray of bran muffins, Alan uses 1/2 cup of oil and 1 egg. Alan has 4 cups of oil and 12 eggs on hand. He sells trays of blueberry muffins for $12 each and trays of bran muffins for $9 each. Alan wants to maximize the money raised at the bake sale. Let x represent the number of blueberry muffins and y represent the number of bran muffins Alan bakes.Speaker’s Clearinghouse must disburse sweepstakeschecks to winners in four different regions of the country:Southeast (SE), Northeast (NE), Far West (FW), andMidwest (MW). The average daily amount of the checkswritten to winners in each region of the country is as follows:SE, $40,000; NE, $60,000; FW, $30,000; MW, $50,000.Speaker’s must issue the checks the day they find out acustomer has won. They can delay winners from quicklycashing their checks by giving a winner a check drawn onan out-of-the-way bank (this will cause the check to clearslowly). Four bank sites are under consideration: FrosbiteFalls, Montana (FF), Redville, South Carolina (R), PaintedForest, Arizona (PF), and Beanville, Maine (B). The annualcost of maintaining an account at each bank is as follows:FF, $50,000; R, $40,000; PF, $30,000; B, $20,000. Eachbank has a requirement that the average daily amount ofchecks written cannot exceed $90,000. The average numberof days it takes a check to clear is given in Table 22.…
- Problem: Acme Manufacturing produces widgets on an assembly line. The assembly process has five tasks, each with its own processing time: Task Processing Time (Seconds) A 10 B 8 C 12 D 9 E 7 drive_spreadsheetExport to Sheets Acme currently has two workers assigned to the assembly line, and they work simultaneously. The company wants to improve line efficiency and reduce waste. Objective: Balance the assembly line by assigning tasks to each worker in a way that minimizes idle time and maximizes output.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.RMC, Inc., is a small firm that produces a variety of chemical products. In a particular production process, three raw materials are blended (mixed together) to produce two products: a fuel additive and a solvent base. Each ton of fuel additive is a mixture of 2/5 ton of material 1 and 3/5 of material 3. A ton of solvent base is a mixture of 1/2 ton of material 1, 1/5 ton of material 2, and 3/10 ton of material 3. After deducting relevant costs, the profit contribution is $40 for every ton of fuel additive produced and $30 for every ton of solvent base produced.RMC’s production is constrained by a limited availability of the three raw materials. For the current production period, RMC has available the following quantities of each raw material:Raw Material Amount Available for ProductionMaterial 1 20 tonsMaterial 2 5 tonsMaterial 3 21 tonsAssuming that RMC is interested in maximizing the total profit contribution, answer the following:i. Compute the value of the objective function…
- RMC, Inc., is a small firm that produces a variety of chemical products. In a particular production process, three raw materials are blended (mixed together) to produce two products: a fuel additive and a solvent base. Each ton of fuel additive is a mixture of 2/5 ton of material 1 and 3/5 of material 3. A ton of solvent base is a mixture of 1/2 ton of material 1, 1/5 ton of material 2, and 3/10 ton of material 3. After deducting relevant costs, the profit contribution is $40 for every ton of fuel additive produced and $30 for every ton of solvent base produced.RMC’s production is constrained by a limited availability of the three raw materials. For the current production period, RMC has available the following quantities of each raw material:Raw Material Amount Available for ProductionMaterial 1 20 tonsMaterial 2 5 tonsMaterial 3 21 tonsAssuming that RMC is interested in maximizing the total profit contribution, answer the following:a. What is the linear programming model for this…The minimum-cost flow problem could be applied_________ Option- 1. by a telephone company attempting to lay out wires in a new housing development. 2. by a forest ranger seeking to minimize the risk of forest fires. 3. None of the choices. 4. by an airline laying out flight routes. 5. All of the choices are correct. Which of the following is not an assumption of a shortest path problem? 1. Associated with each link or arc is a nonnegative number called its length, 2. The objective is to find a shortest path from the origin to the destination. 3. The lines connecting certain pairs of nodes always allow travel in either direction. 4. None of the choices. 5. A path through the network must be chosen going from the origin to the destination.Although the problems say solve graphically, please solve all problems using the QM for Windows software or solve manually. B.6 The Christina Alvarez Company manufactures two lines of designer yard gates, called model A and model B. Every gate requires blending a certain amount of steel and zinc, the company has available a total of 25.000 Ib of steel and 6,000 lb of zinc. Each model A gate requires a mixture of 125 Ib of steel and 20 lb of zinc, and each yields a profit of 590. Each model B gate requires 100 1b of steel and 30 ib of zinc and can be sold for a profit of $70. Find by graphical IP the best production mix of yard gates.